From 92d1df203066ea103cf35a79f645984a90078ca7 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 26 Nov 2020 06:44:00 +0100 Subject: [PATCH] update week 48 --- doc/pub/week48/html/._week48-bs000.html | 233 +++++----- doc/pub/week48/html/._week48-bs001.html | 231 +++++----- doc/pub/week48/html/._week48-bs002.html | 231 +++++----- doc/pub/week48/html/._week48-bs003.html | 231 +++++----- doc/pub/week48/html/._week48-bs004.html | 231 +++++----- doc/pub/week48/html/._week48-bs005.html | 237 +++++----- doc/pub/week48/html/._week48-bs006.html | 254 ++++++----- doc/pub/week48/html/._week48-bs007.html | 248 ++++++----- doc/pub/week48/html/._week48-bs008.html | 269 ++++++----- doc/pub/week48/html/._week48-bs009.html | 443 +++++++------------ doc/pub/week48/html/._week48-bs010.html | 436 ++++++++++++------ doc/pub/week48/html/._week48-bs011.html | 262 ++++++----- doc/pub/week48/html/._week48-bs012.html | 301 ++++++------- doc/pub/week48/html/._week48-bs013.html | 301 ++++++++----- doc/pub/week48/html/._week48-bs014.html | 248 ++++++----- doc/pub/week48/html/._week48-bs015.html | 254 ++++++----- doc/pub/week48/html/._week48-bs016.html | 274 +++++++----- doc/pub/week48/html/._week48-bs017.html | 245 +++++----- doc/pub/week48/html/._week48-bs018.html | 273 ++++++------ doc/pub/week48/html/._week48-bs019.html | 257 +++++------ doc/pub/week48/html/._week48-bs020.html | 257 ++++++----- doc/pub/week48/html/._week48-bs021.html | 274 +++++++----- doc/pub/week48/html/._week48-bs022.html | 261 ++++++----- doc/pub/week48/html/._week48-bs023.html | 246 +++++----- doc/pub/week48/html/._week48-bs024.html | 262 +++++------ doc/pub/week48/html/._week48-bs025.html | 252 ++++++----- doc/pub/week48/html/._week48-bs026.html | 252 +++++------ doc/pub/week48/html/._week48-bs027.html | 260 ++++++----- doc/pub/week48/html/._week48-bs028.html | 258 ++++++----- doc/pub/week48/html/._week48-bs029.html | 251 ++++++----- doc/pub/week48/html/._week48-bs030.html | 251 ++++++----- doc/pub/week48/html/._week48-bs031.html | 268 +++++------ doc/pub/week48/html/._week48-bs032.html | 247 ++++++----- doc/pub/week48/html/._week48-bs033.html | 257 ++++++----- doc/pub/week48/html/._week48-bs034.html | 263 ++++++----- doc/pub/week48/html/._week48-bs035.html | 265 ++++++----- doc/pub/week48/html/._week48-bs036.html | 270 +++++------ doc/pub/week48/html/._week48-bs037.html | 242 +++++----- doc/pub/week48/html/._week48-bs038.html | 266 ++++++----- doc/pub/week48/html/._week48-bs039.html | 272 +++++++----- doc/pub/week48/html/._week48-bs040.html | 251 +++++------ doc/pub/week48/html/._week48-bs041.html | 259 +++++------ doc/pub/week48/html/._week48-bs042.html | 276 ++++++------ doc/pub/week48/html/._week48-bs043.html | 261 ++++++----- doc/pub/week48/html/._week48-bs044.html | 269 +++++------ doc/pub/week48/html/._week48-bs045.html | 271 +++++++----- doc/pub/week48/html/._week48-bs046.html | 271 ++++++------ doc/pub/week48/html/._week48-bs047.html | 271 +++++++----- doc/pub/week48/html/._week48-bs048.html | 256 ++++++----- doc/pub/week48/html/._week48-bs049.html | 269 ++++++----- doc/pub/week48/html/._week48-bs050.html | 248 ++++++----- doc/pub/week48/html/._week48-bs051.html | 252 ++++++----- doc/pub/week48/html/._week48-bs052.html | 261 +++++------ doc/pub/week48/html/._week48-bs053.html | 257 +++++------ doc/pub/week48/html/._week48-bs054.html | 265 +++++------ doc/pub/week48/html/._week48-bs055.html | 264 ++++++----- doc/pub/week48/html/._week48-bs056.html | 259 ++++++----- doc/pub/week48/html/._week48-bs057.html | 270 ++++++----- doc/pub/week48/html/._week48-bs058.html | 257 ++++++----- doc/pub/week48/html/._week48-bs059.html | 246 +++++----- doc/pub/week48/html/._week48-bs060.html | 249 ++++++----- doc/pub/week48/html/week48-bs.html | 233 +++++----- doc/pub/week48/html/week48-reveal.html | 223 +++++++--- doc/pub/week48/html/week48-solarized.html | 336 +++++++++----- doc/pub/week48/html/week48.html | 336 +++++++++----- doc/pub/week48/ipynb/ipynb-week48-src.tar.gz | Bin 822634 -> 822634 bytes doc/pub/week48/ipynb/week48.ipynb | 135 +++++- doc/src/week48/week48.do.txt | 103 ++++- 68 files changed, 9515 insertions(+), 7966 deletions(-) diff --git a/doc/pub/week48/html/._week48-bs000.html b/doc/pub/week48/html/._week48-bs000.html index 341424093..dc68b9446 100644 --- a/doc/pub/week48/html/._week48-bs000.html +++ b/doc/pub/week48/html/._week48-bs000.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
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  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
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  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
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  • Perspective on Machine Learning
    • -
  • Machine Learning Research
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  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
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  • Optimization Methods and Hyperparameters
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  • Resampling
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  • Other courses on Data science and Machine Learning at UiO
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  • Additional courses of interest
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  • What's the future like?
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  • Types of Machine Learning, a repetition
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  • Why Boltzmann machines?
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  • Boltzmann Machines
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  • Some similarities and differences from DNNs
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  • Boltzmann machines (BM)
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  • A standard BM setup
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  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
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  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
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  • Bayesian Machine Learning
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  • Reinforcement Learning
    • -
  • Transfer learning
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  • Adversarial learning
    • -
  • Dual learning
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  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -260,7 +277,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 25, 2020

    +

    Nov 26, 2020


    @@ -284,7 +301,7 @@ MathJax.Hub.Config({

  • 9
  • 10
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs001.html b/doc/pub/week48/html/._week48-bs001.html index f543da998..709495f24 100644 --- a/doc/pub/week48/html/._week48-bs001.html +++ b/doc/pub/week48/html/._week48-bs001.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
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    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
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  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
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  • Learning outcomes and overarching aims of this course
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  • Perspective on Machine Learning
    • -
  • Machine Learning Research
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    • -
  • Which Activation and Weights to Choose in Neural Networks
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  • Optimization Methods and Hyperparameters
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  • Types of Machine Learning, a repetition
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  • Why Boltzmann machines?
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    • -
  • Some similarities and differences from DNNs
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  • Boltzmann machines (BM)
    • -
  • A standard BM setup
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  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
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  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
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  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -267,7 +284,7 @@ Geron's chapter 5. Chapter 12 (sections 12.1-12.3 are the most relevant ones) o
  • 10
  • 11
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs002.html b/doc/pub/week48/html/._week48-bs002.html index 7b26e51fb..cd19ad1f4 100644 --- a/doc/pub/week48/html/._week48-bs002.html +++ b/doc/pub/week48/html/._week48-bs002.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
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  • Different kernels and Mercer's theorem
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  • The moons example
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  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
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  • What? Me worry? No final exam in this course!
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  • Topics we have covered this year
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  • Statistical analysis and optimization of data
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  • Machine learning
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  • Learning outcomes and overarching aims of this course
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  • Perspective on Machine Learning
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  • Machine Learning Research
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  • Choose a Model and Algorithm
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  • Which Activation and Weights to Choose in Neural Networks
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  • Optimization Methods and Hyperparameters
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  • Resampling
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  • Other courses on Data science and Machine Learning at UiO
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  • What's the future like?
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  • Types of Machine Learning, a repetition
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  • Why Boltzmann machines?
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  • Boltzmann Machines
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  • Some similarities and differences from DNNs
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  • Boltzmann machines (BM)
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  • A standard BM setup
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  • The structure of the RBM network
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  • The network
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  • Goals
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  • Joint distribution
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  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
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  • Bayesian Machine Learning
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  • Reinforcement Learning
    • -
  • Transfer learning
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  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
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  • The Challenges Facing Machine Learning
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  • Explainable machine learning
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  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -264,7 +281,7 @@ We finalize our discussion on Support Vector Machines with an emphasis on kernel
  • 11
  • 12
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs003.html b/doc/pub/week48/html/._week48-bs003.html index 78aa8373d..8168b3b23 100644 --- a/doc/pub/week48/html/._week48-bs003.html +++ b/doc/pub/week48/html/._week48-bs003.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? 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  • Different kernels and Mercer's theorem
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  • Mathematical optimization of convex functions
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  • How do we solve these problems?
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  • A simple example
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  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -267,7 +284,7 @@ modern research projects in machine learning.
  • 12
  • 13
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs004.html b/doc/pub/week48/html/._week48-bs004.html index 1ff3f2dbf..9e890d393 100644 --- a/doc/pub/week48/html/._week48-bs004.html +++ b/doc/pub/week48/html/._week48-bs004.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -285,7 +302,7 @@ problems. I recommend you take a look at the lectures from last week on the bin
  • 13
  • 14
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs005.html b/doc/pub/week48/html/._week48-bs005.html index 327799f92..30a97c438 100644 --- a/doc/pub/week48/html/._week48-bs005.html +++ b/doc/pub/week48/html/._week48-bs005.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
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    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -253,13 +270,13 @@ wavelets, splines etc.

    If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +here generated by the code below (see also Figures 12.2 and 12.3 of Hastie et al.), we can achieve a better separation by introducing more complex +basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to obtain a separation between the classes which is almost linear.

    The change of basis, from \( x\rightarrow z=\phi(x) \) leads to the same type of equations to be solved, except that -we need to introduce for example a polynomial transformation to a two-dimensional training set. +we need to introduce, for example, a polynomial transformation to a two-dimensional training set.

    @@ -332,7 +349,7 @@ plt.show()

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    • diff --git a/doc/pub/week48/html/._week48-bs006.html b/doc/pub/week48/html/._week48-bs006.html index 676cddb39..5a086a8d8 100644 --- a/doc/pub/week48/html/._week48-bs006.html +++ b/doc/pub/week48/html/._week48-bs006.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -246,7 +263,7 @@ MathJax.Hub.Config({

    Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables) $$ -z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right). +z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right). $$

    @@ -257,7 +274,7 @@ $$ subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \), and for the support vectors $$ -y_i(\boldsymbol{w}^T\boldsymbol{z}_i+b)= 1 \hspace{0.1cm}\forall i, +y_i(\boldsymbol{z}_i^T\boldsymbol{w}+b)= 1 \hspace{0.1cm}\forall i, $$ from which we also find \( b \). @@ -268,20 +285,21 @@ $$ For the above example, the kernel reads $$ -K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2. +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} 1\\ \sqrt{2}x_j \\ \sqrt{2}y_j \\ x_j^2\\ y_i^2\\ \sqrt{2}x_jy_j \end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j. $$

    -We note that this is nothing but the dot product of the two original -vectors \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). Instead of thus computing the -product in the Lagrangian of \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we simply compute -the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). +We note that this dot product can be rewritten as +$$ +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d, +$$ -

    +where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \). +To compute the last equation is however inefficient from a computational stand. +Instead of computing the last equation for the kernel, we simply compute +the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). This leads to the so-called -kernel trick and the result leads to the same as if we went through -the trouble of performing the transformation -\( \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j) \) during the SVM calculations. +kernel trick.

    @@ -305,7 +323,7 @@ the trouble of performing the transformation

  • 15
  • 16
  • ...
    • -
  • 61
    • +
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    • diff --git a/doc/pub/week48/html/._week48-bs007.html b/doc/pub/week48/html/._week48-bs007.html index fa45911f6..bd4e0a5f0 100644 --- a/doc/pub/week48/html/._week48-bs007.html +++ b/doc/pub/week48/html/._week48-bs007.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -242,7 +259,9 @@ MathJax.Hub.Config({

    The problem to solve

    -Using our definition of the kernel We can rewrite again the Lagrangian + +

    +Using our definition of the kernel, we can rewrite again the Lagrangian $$ {\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{z}_j, $$ @@ -261,19 +280,6 @@ subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vec \( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). If we add the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \). -

    -We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type -$$ -\begin{align*} - &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber - &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. -\end{align*} -$$ - -Below we discuss how to solve these equations. Here we note that the matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). -Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \). How to set up the matrix \( \boldsymbol{G} \) is discussed later. Here note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into -\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \). -

    @@ -297,7 +303,7 @@ Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.

  • 16
  • 17
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs008.html b/doc/pub/week48/html/._week48-bs008.html index 22ccb60b2..212170c3c 100644 --- a/doc/pub/week48/html/._week48-bs008.html +++ b/doc/pub/week48/html/._week48-bs008.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -241,40 +258,20 @@ MathJax.Hub.Config({ -

    Different kernels and Mercer's theorem

    +

    Tailoring the equations to the usage of CVXOPT

    -There are several popular kernels being used. These are - -

      -
    1. Linear: \( K(\boldsymbol{x},\boldsymbol{y})=\boldsymbol{x}^T\boldsymbol{y} \),
      2. -
    2. Polynomial: \( K(\boldsymbol{x},\boldsymbol{y})=(\boldsymbol{x}^T\boldsymbol{y}+\gamma)^d \),
      3. -
    3. Gaussian Radial Basis Function: \( K(\boldsymbol{x},\boldsymbol{y})=\exp{\left(-\gamma\vert\vert\boldsymbol{x}-\boldsymbol{y}\vert\vert^2\right)} \),
      4. -
    4. Tanh: \( K(\boldsymbol{x},\boldsymbol{y})=\tanh{(\boldsymbol{x}^T\boldsymbol{y}+\gamma)} \),
      5. -
    - -and many other ones. - -

    -An important theorem for us is Mercer's -theorem. The -theorem states that if a kernel function \( K \) is symmetric, continuous -and leads to a positive semi-definite matrix \( \boldsymbol{P} \) then there -exists a function \( \phi \) that maps \( \boldsymbol{x}_i \) and \( \boldsymbol{x}_j \) into -another space (possibly with much higher dimensions) such that - +We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type $$ -K(\boldsymbol{x}_i,\boldsymbol{x}_j)=\phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j). +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. +\end{align*} $$ -

    -So you can use \( K \) as a kernel since you know \( \phi \) exists, even if -you don’t know what \( \phi \) is. - -

    -Note that some frequently used kernels (such as the Sigmoid kernel) -don’t respect all of Mercer’s conditions, yet they generally work well -in practice. +Below we discuss how to solve these equations. Here we note that the matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). +Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \). How to set up the matrix \( \boldsymbol{G} \) is discussed later. Here note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into +\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).

    @@ -300,7 +297,7 @@ in practice.

  • 17
  • 18
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs009.html b/doc/pub/week48/html/._week48-bs009.html index 66b4ab0d9..b6b72dce2 100644 --- a/doc/pub/week48/html/._week48-bs009.html +++ b/doc/pub/week48/html/._week48-bs009.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -241,199 +258,41 @@ MathJax.Hub.Config({ -

    The moons example

    +

    Different kernels and Mercer's theorem

    +

    +There are several popular kernels being used. These are - -

    from __future__ import division, print_function, unicode_literals
+
      
+
    1.  Linear: \( K(\boldsymbol{x},\boldsymbol{y})=\boldsymbol{x}^T\boldsymbol{y} \),
      2. 
+
    2.  Polynomial: \( K(\boldsymbol{x},\boldsymbol{y})=(\boldsymbol{x}^T\boldsymbol{y}+\gamma)^d \),
      3. 
+
    3.  Gaussian Radial Basis Function: \( K(\boldsymbol{x},\boldsymbol{y})=\exp{\left(-\gamma\vert\vert\boldsymbol{x}-\boldsymbol{y}\vert\vert^2\right)} \),
      4. 
+
    4.  Tanh: \( K(\boldsymbol{x},\boldsymbol{y})=\tanh{(\boldsymbol{x}^T\boldsymbol{y}+\gamma)} \),
      5. 
+
    
 
-import numpy as np
-np.random.seed(42)
+and many other ones.
 
-import matplotlib
-import matplotlib.pyplot as plt
-plt.rcParams['axes.labelsize'] = 14
-plt.rcParams['xtick.labelsize'] = 12
-plt.rcParams['ytick.labelsize'] = 12
+
    
+An important theorem for us is Mercer's
+theorem.  The
+theorem states that if a kernel function \( K \) is symmetric, continuous
+and leads to a positive semi-definite matrix \( \boldsymbol{P} \) then there
+exists a function \( \phi \) that maps \( \boldsymbol{x}_i \) and \( \boldsymbol{x}_j \) into
+another space (possibly with much higher dimensions) such that
 
+$$
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=\phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j).
+$$
 
-from sklearn.svm import SVC
-from sklearn import datasets
+
    
+So you can use \( K \) as a kernel since you know \( \phi \) exists, even if
+you don’t know what \( \phi \) is.
 
+
    
+Note that some frequently used kernels (such as the Sigmoid kernel)
+don’t respect all of Mercer’s conditions, yet they generally work well
+in practice.
 
-
-from sklearn.pipeline import Pipeline
-from sklearn.preprocessing import StandardScaler
-from sklearn.svm import LinearSVC
-
-
-from sklearn.datasets import make_moons
-X, y = make_moons(n_samples=100, noise=0.15, random_state=42)
-
-def plot_dataset(X, y, axes):
-    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
-    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
-    plt.axis(axes)
-    plt.grid(True, which='both')
-    plt.xlabel(r"$x_1$", fontsize=20)
-    plt.ylabel(r"$x_2$", fontsize=20, rotation=0)
-
-plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
-plt.show()
-
-from sklearn.datasets import make_moons
-from sklearn.pipeline import Pipeline
-from sklearn.preprocessing import PolynomialFeatures
-
-polynomial_svm_clf = Pipeline([
-        ("poly_features", PolynomialFeatures(degree=3)),
-        ("scaler", StandardScaler()),
-        ("svm_clf", LinearSVC(C=10, loss="hinge", random_state=42))
-    ])
-
-polynomial_svm_clf.fit(X, y)
-
-def plot_predictions(clf, axes):
-    x0s = np.linspace(axes[0], axes[1], 100)
-    x1s = np.linspace(axes[2], axes[3], 100)
-    x0, x1 = np.meshgrid(x0s, x1s)
-    X = np.c_[x0.ravel(), x1.ravel()]
-    y_pred = clf.predict(X).reshape(x0.shape)
-    y_decision = clf.decision_function(X).reshape(x0.shape)
-    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)
-    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)
-
-plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])
-plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
-
-plt.show()
-
-
-from sklearn.svm import SVC
-
-poly_kernel_svm_clf = Pipeline([
-        ("scaler", StandardScaler()),
-        ("svm_clf", SVC(kernel="poly", degree=3, coef0=1, C=5))
-    ])
-poly_kernel_svm_clf.fit(X, y)
-
-poly100_kernel_svm_clf = Pipeline([
-        ("scaler", StandardScaler()),
-        ("svm_clf", SVC(kernel="poly", degree=10, coef0=100, C=5))
-    ])
-poly100_kernel_svm_clf.fit(X, y)
-
-plt.figure(figsize=(11, 4))
-
-plt.subplot(121)
-plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
-plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
-plt.title(r"$d=3, r=1, C=5$", fontsize=18)
-
-plt.subplot(122)
-plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
-plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
-plt.title(r"$d=10, r=100, C=5$", fontsize=18)
-
-plt.show()
-
-def gaussian_rbf(x, landmark, gamma):
-    return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1)**2)
-
-gamma = 0.3
-
-x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)
-x2s = gaussian_rbf(x1s, -2, gamma)
-x3s = gaussian_rbf(x1s, 1, gamma)
-
-XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]
-yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])
-
-plt.figure(figsize=(11, 4))
-
-plt.subplot(121)
-plt.grid(True, which='both')
-plt.axhline(y=0, color='k')
-plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c="red")
-plt.plot(X1D[:, 0][yk==0], np.zeros(4), "bs")
-plt.plot(X1D[:, 0][yk==1], np.zeros(5), "g^")
-plt.plot(x1s, x2s, "g--")
-plt.plot(x1s, x3s, "b:")
-plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])
-plt.xlabel(r"$x_1$", fontsize=20)
-plt.ylabel(r"Similarity", fontsize=14)
-plt.annotate(r'$\mathbf{x}$',
-             xy=(X1D[3, 0], 0),
-             xytext=(-0.5, 0.20),
-             ha="center",
-             arrowprops=dict(facecolor='black', shrink=0.1),
-             fontsize=18,
-            )
-plt.text(-2, 0.9, "$x_2$", ha="center", fontsize=20)
-plt.text(1, 0.9, "$x_3$", ha="center", fontsize=20)
-plt.axis([-4.5, 4.5, -0.1, 1.1])
-
-plt.subplot(122)
-plt.grid(True, which='both')
-plt.axhline(y=0, color='k')
-plt.axvline(x=0, color='k')
-plt.plot(XK[:, 0][yk==0], XK[:, 1][yk==0], "bs")
-plt.plot(XK[:, 0][yk==1], XK[:, 1][yk==1], "g^")
-plt.xlabel(r"$x_2$", fontsize=20)
-plt.ylabel(r"$x_3$  ", fontsize=20, rotation=0)
-plt.annotate(r'$\phi\left(\mathbf{x}\right)$',
-             xy=(XK[3, 0], XK[3, 1]),
-             xytext=(0.65, 0.50),
-             ha="center",
-             arrowprops=dict(facecolor='black', shrink=0.1),
-             fontsize=18,
-            )
-plt.plot([-0.1, 1.1], [0.57, -0.1], "r--", linewidth=3)
-plt.axis([-0.1, 1.1, -0.1, 1.1])
-    
-plt.subplots_adjust(right=1)
-
-plt.show()
-
-
-x1_example = X1D[3, 0]
-for landmark in (-2, 1):
-    k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)
-    print("Phi({}, {}) = {}".format(x1_example, landmark, k))
-
-rbf_kernel_svm_clf = Pipeline([
-        ("scaler", StandardScaler()),
-        ("svm_clf", SVC(kernel="rbf", gamma=5, C=0.001))
-    ])
-rbf_kernel_svm_clf.fit(X, y)
-
-
-from sklearn.svm import SVC
-
-gamma1, gamma2 = 0.1, 5
-C1, C2 = 0.001, 1000
-hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)
-
-svm_clfs = []
-for gamma, C in hyperparams:
-    rbf_kernel_svm_clf = Pipeline([
-            ("scaler", StandardScaler()),
-            ("svm_clf", SVC(kernel="rbf", gamma=gamma, C=C))
-        ])
-    rbf_kernel_svm_clf.fit(X, y)
-    svm_clfs.append(rbf_kernel_svm_clf)
-
-plt.figure(figsize=(11, 7))
-
-for i, svm_clf in enumerate(svm_clfs):
-    plt.subplot(221 + i)
-    plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])
-    plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
-    gamma, C = hyperparams[i]
-    plt.title(r"$\gamma = {}, C = {}$".format(gamma, C), fontsize=16)
-
-plt.show()
-

    @@ -459,7 +318,7 @@ plt.show()

  • 18
  • 19
  • ...
    • -
  • 61
    • +
  • 64
  • »
    • diff --git a/doc/pub/week48/html/._week48-bs010.html b/doc/pub/week48/html/._week48-bs010.html index 14ddcefce..e1b4e9138 100644 --- a/doc/pub/week48/html/._week48-bs010.html +++ b/doc/pub/week48/html/._week48-bs010.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -241,28 +258,199 @@ MathJax.Hub.Config({ -

    Mathematical optimization of convex functions

    - +

    The moons example (Adapted from Geron, chapter 5)

    -A mathematical (quadratic) optimization problem, or just optimization problem, has the form -$$ -\begin{align*} - &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber - &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. -\end{align*} -$$ -subject to some constraints for say a selected set \( i=1,2,\dots, n \). -In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the -vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with. + +

    from __future__ import division, print_function, unicode_literals
 
-
    
-In our case we are particularly interested in a class of optimization problems called convex optmization problems. 
-In our discussion on gradient descent methods we discussed at length the definition of a convex function.
+import numpy as np
+np.random.seed(42)
 
-
    
-Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics.
+import matplotlib
+import matplotlib.pyplot as plt
+plt.rcParams['axes.labelsize'] = 14
+plt.rcParams['xtick.labelsize'] = 12
+plt.rcParams['ytick.labelsize'] = 12
 
+
+from sklearn.svm import SVC
+from sklearn import datasets
+
+
+
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import StandardScaler
+from sklearn.svm import LinearSVC
+
+
+from sklearn.datasets import make_moons
+X, y = make_moons(n_samples=100, noise=0.15, random_state=42)
+
+def plot_dataset(X, y, axes):
+    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
+    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
+    plt.axis(axes)
+    plt.grid(True, which='both')
+    plt.xlabel(r"$x_1$", fontsize=20)
+    plt.ylabel(r"$x_2$", fontsize=20, rotation=0)
+
+plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
+plt.show()
+
+from sklearn.datasets import make_moons
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import PolynomialFeatures
+
+polynomial_svm_clf = Pipeline([
+        ("poly_features", PolynomialFeatures(degree=3)),
+        ("scaler", StandardScaler()),
+        ("svm_clf", LinearSVC(C=10, loss="hinge", random_state=42))
+    ])
+
+polynomial_svm_clf.fit(X, y)
+
+def plot_predictions(clf, axes):
+    x0s = np.linspace(axes[0], axes[1], 100)
+    x1s = np.linspace(axes[2], axes[3], 100)
+    x0, x1 = np.meshgrid(x0s, x1s)
+    X = np.c_[x0.ravel(), x1.ravel()]
+    y_pred = clf.predict(X).reshape(x0.shape)
+    y_decision = clf.decision_function(X).reshape(x0.shape)
+    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)
+    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)
+
+plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])
+plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
+
+plt.show()
+
+
+from sklearn.svm import SVC
+
+poly_kernel_svm_clf = Pipeline([
+        ("scaler", StandardScaler()),
+        ("svm_clf", SVC(kernel="poly", degree=3, coef0=1, C=5))
+    ])
+poly_kernel_svm_clf.fit(X, y)
+
+poly100_kernel_svm_clf = Pipeline([
+        ("scaler", StandardScaler()),
+        ("svm_clf", SVC(kernel="poly", degree=10, coef0=100, C=5))
+    ])
+poly100_kernel_svm_clf.fit(X, y)
+
+plt.figure(figsize=(11, 4))
+
+plt.subplot(121)
+plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
+plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
+plt.title(r"$d=3, r=1, C=5$", fontsize=18)
+
+plt.subplot(122)
+plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])
+plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
+plt.title(r"$d=10, r=100, C=5$", fontsize=18)
+
+plt.show()
+
+def gaussian_rbf(x, landmark, gamma):
+    return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1)**2)
+
+gamma = 0.3
+
+x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)
+x2s = gaussian_rbf(x1s, -2, gamma)
+x3s = gaussian_rbf(x1s, 1, gamma)
+
+XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]
+yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])
+
+plt.figure(figsize=(11, 4))
+
+plt.subplot(121)
+plt.grid(True, which='both')
+plt.axhline(y=0, color='k')
+plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c="red")
+plt.plot(X1D[:, 0][yk==0], np.zeros(4), "bs")
+plt.plot(X1D[:, 0][yk==1], np.zeros(5), "g^")
+plt.plot(x1s, x2s, "g--")
+plt.plot(x1s, x3s, "b:")
+plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])
+plt.xlabel(r"$x_1$", fontsize=20)
+plt.ylabel(r"Similarity", fontsize=14)
+plt.annotate(r'$\mathbf{x}$',
+             xy=(X1D[3, 0], 0),
+             xytext=(-0.5, 0.20),
+             ha="center",
+             arrowprops=dict(facecolor='black', shrink=0.1),
+             fontsize=18,
+            )
+plt.text(-2, 0.9, "$x_2$", ha="center", fontsize=20)
+plt.text(1, 0.9, "$x_3$", ha="center", fontsize=20)
+plt.axis([-4.5, 4.5, -0.1, 1.1])
+
+plt.subplot(122)
+plt.grid(True, which='both')
+plt.axhline(y=0, color='k')
+plt.axvline(x=0, color='k')
+plt.plot(XK[:, 0][yk==0], XK[:, 1][yk==0], "bs")
+plt.plot(XK[:, 0][yk==1], XK[:, 1][yk==1], "g^")
+plt.xlabel(r"$x_2$", fontsize=20)
+plt.ylabel(r"$x_3$  ", fontsize=20, rotation=0)
+plt.annotate(r'$\phi\left(\mathbf{x}\right)$',
+             xy=(XK[3, 0], XK[3, 1]),
+             xytext=(0.65, 0.50),
+             ha="center",
+             arrowprops=dict(facecolor='black', shrink=0.1),
+             fontsize=18,
+            )
+plt.plot([-0.1, 1.1], [0.57, -0.1], "r--", linewidth=3)
+plt.axis([-0.1, 1.1, -0.1, 1.1])
+    
+plt.subplots_adjust(right=1)
+
+plt.show()
+
+
+x1_example = X1D[3, 0]
+for landmark in (-2, 1):
+    k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)
+    print("Phi({}, {}) = {}".format(x1_example, landmark, k))
+
+rbf_kernel_svm_clf = Pipeline([
+        ("scaler", StandardScaler()),
+        ("svm_clf", SVC(kernel="rbf", gamma=5, C=0.001))
+    ])
+rbf_kernel_svm_clf.fit(X, y)
+
+
+from sklearn.svm import SVC
+
+gamma1, gamma2 = 0.1, 5
+C1, C2 = 0.001, 1000
+hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)
+
+svm_clfs = []
+for gamma, C in hyperparams:
+    rbf_kernel_svm_clf = Pipeline([
+            ("scaler", StandardScaler()),
+            ("svm_clf", SVC(kernel="rbf", gamma=gamma, C=C))
+        ])
+    rbf_kernel_svm_clf.fit(X, y)
+    svm_clfs.append(rbf_kernel_svm_clf)
+
+plt.figure(figsize=(11, 7))
+
+for i, svm_clf in enumerate(svm_clfs):
+    plt.subplot(221 + i)
+    plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])
+    plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
+    gamma, C = hyperparams[i]
+    plt.title(r"$\gamma = {}, C = {}$".format(gamma, C), fontsize=16)
+
+plt.show()
+

    @@ -289,7 +477,7 @@ Convex optimization problems play a central role in applied mathematics and we r

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    • diff --git a/doc/pub/week48/html/._week48-bs011.html b/doc/pub/week48/html/._week48-bs011.html index d3e4ed1b1..9d1d38af1 100644 --- a/doc/pub/week48/html/._week48-bs011.html +++ b/doc/pub/week48/html/._week48-bs011.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -241,28 +258,27 @@ MathJax.Hub.Config({ -

    How do we solve these problems?

    +

    Mathematical optimization of convex functions

    -If we use Python as programming language and wish to venture beyond -scikit-learn, tensorflow and similar software which makes our -lives so much easier, we need to dive into the wonderful world of -quadratic programming. We can, if we wish, solve the minimization -problem using say standard gradient methods or conjugate gradient -methods. However, these methods tend to exhibit a rather slow -converge. So, welcome to the promised land of quadratic programming. +A mathematical (quadratic) optimization problem, or just optimization problem, has the form +$$ +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. +\end{align*} +$$ + +subject to some constraints for say a selected set \( i=1,2,\dots, n \). +In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the +vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with.

    -The functions we need are contained in the quadratic programming package CVXOPT and we need to import it together with numpy as +In our case we are particularly interested in a class of optimization problems called convex optmization problems. +In our discussion on gradient descent methods we discussed at length the definition of a convex function.

    - - -

    import numpy
-import cvxopt
-
    -

    -This will make our life much easier. You don't need t write your own optimizer. +Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics.

    @@ -290,7 +306,7 @@ This will make our life much easier. You don't need t write your own optimizer.

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    • diff --git a/doc/pub/week48/html/._week48-bs012.html b/doc/pub/week48/html/._week48-bs012.html index 9eb0b7373..e8fc6bc04 100644 --- a/doc/pub/week48/html/._week48-bs012.html +++ b/doc/pub/week48/html/._week48-bs012.html @@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -173,59 +187,62 @@ MathJax.Hub.Config({
  • Kernels and non-linearity
  • The equations
  • The problem to solve
    • -
  • Different kernels and Mercer's theorem
    • -
  • The moons example
    • -
  • Mathematical optimization of convex functions
    • -
  • How do we solve these problems?
    • -
  • A simple example
    • -
  • Back to the more realistic cases
    • -
  • Summary of course
    • -
  • What? Me worry? No final exam in this course!
    • -
  • Topics we have covered this year
    • -
  • Statistical analysis and optimization of data
    • -
  • Machine learning
    • -
  • Learning outcomes and overarching aims of this course
    • -
  • Perspective on Machine Learning
    • -
  • Machine Learning Research
    • -
  • Starting your Machine Learning Project
    • -
  • Choose a Model and Algorithm
    • -
  • Preparing Your Data
    • -
  • Which Activation and Weights to Choose in Neural Networks
    • -
  • Optimization Methods and Hyperparameters
    • -
  • Resampling
    • -
  • Other courses on Data science and Machine Learning at UiO
    • -
  • Additional courses of interest
    • -
  • What's the future like?
    • -
  • Types of Machine Learning, a repetition
    • -
  • Why Boltzmann machines?
    • -
  • Boltzmann Machines
    • -
  • Some similarities and differences from DNNs
    • -
  • Boltzmann machines (BM)
    • -
  • A standard BM setup
    • -
  • The structure of the RBM network
    • -
  • The network
    • -
  • Goals
    • -
  • Joint distribution
    • -
  • Network Elements, the energy function
    • -
  • Defining different types of RBMs
    • -
  • More about RBMs
    • -
  • Autoencoders: Overarching view
    • -
  • Bayesian Machine Learning
    • -
  • Reinforcement Learning
    • -
  • Transfer learning
    • -
  • Adversarial learning
    • -
  • Dual learning
    • -
  • Distributed machine learning
    • -
  • Meta learning
    • -
  • The Challenges Facing Machine Learning
    • -
  • Explainable machine learning
    • -
  • Quantum machine learning
    • -
  • Quantum machine learning algorithms based on linear algebra
    • -
  • Quantum reinforcement learning
    • -
  • Quantum deep learning
    • -
  • Social machine learning
    • -
  • The last words?
    • -
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • +
  • Tailoring the equations to the usage of CVXOPT
    • +
  • Different kernels and Mercer's theorem
    • +
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems?
    • +
  • A simple example
    • +
  • Back to the more realistic cases
    • +
  • Setting up the matrices and the problem
    • +
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • +
  • Summary of course
    • +
  • What? Me worry? No final exam in this course!
    • +
  • Topics we have covered this year
    • +
  • Statistical analysis and optimization of data
    • +
  • Machine learning
    • +
  • Learning outcomes and overarching aims of this course
    • +
  • Perspective on Machine Learning
    • +
  • Machine Learning Research
    • +
  • Starting your Machine Learning Project
    • +
  • Choose a Model and Algorithm
    • +
  • Preparing Your Data
    • +
  • Which Activation and Weights to Choose in Neural Networks
    • +
  • Optimization Methods and Hyperparameters
    • +
  • Resampling
    • +
  • Other courses on Data science and Machine Learning at UiO
    • +
  • Additional courses of interest
    • +
  • What's the future like?
    • +
  • Types of Machine Learning, a repetition
    • +
  • Why Boltzmann machines?
    • +
  • Boltzmann Machines
    • +
  • Some similarities and differences from DNNs
    • +
  • Boltzmann machines (BM)
    • +
  • A standard BM setup
    • +
  • The structure of the RBM network
    • +
  • The network
    • +
  • Goals
    • +
  • Joint distribution
    • +
  • Network Elements, the energy function
    • +
  • Defining different types of RBMs
    • +
  • More about RBMs
    • +
  • Autoencoders: Overarching view
    • +
  • Bayesian Machine Learning
    • +
  • Reinforcement Learning
    • +
  • Transfer learning
    • +
  • Adversarial learning
    • +
  • Dual learning
    • +
  • Distributed machine learning
    • +
  • Meta learning
    • +
  • The Challenges Facing Machine Learning
    • +
  • Explainable machine learning
    • +
  • Quantum machine learning
    • +
  • Quantum machine learning algorithms based on linear algebra
    • +
  • Quantum reinforcement learning
    • +
  • Quantum deep learning
    • +
  • Social machine learning
    • +
  • The last words?
    • +
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • @@ -241,71 +258,29 @@ MathJax.Hub.Config({ -

    A simple example

    +

    How do we solve these problems?

    -We remind ourselves about the general problem we want to solve -$$ -\begin{align*} - &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber - &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f. -\end{align*} -$$ +If we use Python as programming language and wish to venture beyond +scikit-learn, tensorflow and similar software which makes our +lives so much easier, we need to dive into the wonderful world of +quadratic programming. We can, if we wish, solve the minimization +problem using say standard gradient methods or conjugate gradient +methods. However, these methods tend to exhibit a rather slow +converge. So, welcome to the promised land of quadratic programming.

    -Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem -$$ -\begin{align*} - &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber - &\mathrm{subject to} \\ \nonumber - &x, y \geq 0 \\ \nonumber - &x+3y \geq 15 \\ \nonumber - &2x+5y \leq 100 \\ \nonumber - &3x+4y \leq 80. \\ \nonumber -\end{align*} -$$ +The functions we need are contained in the quadratic programming package CVXOPT and we need to import it together with numpy as -The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns) -$$ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. -$$ - -Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation -$$ -\begin{bmatrix} -1 & 0 \\ 0 & -1 \\ -1 & -3 \\ 2 & 5 \\ 3 & 4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} \preceq \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}. -$$ - -We have collapsed all the inequalities into a single matrix \( \boldsymbol{G} \). We see also that our matrix -$$ -\boldsymbol{P} =\begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} -$$ - -is clearly positive semi-definite (all eigenvalues larger or equal zero). -Finally, the vector \( \boldsymbol{h} \) is defined as -$$ -\boldsymbol{h} = \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}. -$$ - -

    -Since we don't have any equalities the matrix \( \boldsymbol{A} \) is set to zero -The following code solves the equations for us

    -

    # Import the necessary packages
-import numpy
-from cvxopt import matrix
-from cvxopt import solvers
-P = matrix(numpy.diag([1,0]), tc=’d’)
-q = matrix(numpy.array([3,4]), tc=’d’)
-G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
-h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
-# Construct the QP, invoke solver
-sol = solvers.qp(P,q,G,h)
-# Extract optimal value and solution
-sol[’x’] 
-sol[’primal objective’]
+
    import numpy
+import cvxopt
 
    
+
    
+This will make our life much easier. You don't need to write your own optimizer.
+
 
    
 
    
 
@@ -332,7 +307,7 @@ sol[’primal objective’]
   
  • 21
    • 
   
  • 22
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs013.html b/doc/pub/week48/html/._week48-bs013.html
index 55fb74f4a..3c1d564b3 100644
--- a/doc/pub/week48/html/._week48-bs013.html
+++ b/doc/pub/week48/html/._week48-bs013.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,23 +258,71 @@ MathJax.Hub.Config({
 
 
 
-
    Back to the more realistic cases 
    
+
    A simple example 
    
 
 
    
-We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the slack parameter \( C \) we have
+We remind ourselves about the general problem we want to solve
 $$
-\frac{1}{2} \boldsymbol{\lambda}^T\begin{bmatrix} y_1y_1K(\boldsymbol{x}_1,\boldsymbol{x}_1) & y_1y_2K(\boldsymbol{x}_1,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_1,\boldsymbol{x}_n) \\
-y_2y_1K(\boldsymbol{x}_2,\boldsymbol{x}_1) & y_2y_2K(\boldsymbol{x}_2,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_2,\boldsymbol{x}_n) \\
-\dots & \dots & \dots & \dots & \dots \\
-\dots & \dots & \dots & \dots & \dots \\
-y_ny_1K(\boldsymbol{x}_n,\boldsymbol{x}_1) & y_ny_2K(\boldsymbol{x}_n\boldsymbol{x}_2) & \dots & \dots & y_ny_nK(\boldsymbol{x}_n,\boldsymbol{x}_n) \\
-\end{bmatrix}\boldsymbol{\lambda}-\mathbb{I}\boldsymbol{\lambda}, 
+\begin{align*}
+    &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber
+    &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge  \boldsymbol{A}\boldsymbol{x}=f.
+\end{align*}
 $$
 
-subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and 
-\( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). 
-With  the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
+
    
+Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
+$$
+\begin{align*}
+    &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
+    &\mathrm{subject to} \\ \nonumber
+    &x, y \geq 0 \\ \nonumber
+    &x+3y  \geq 15 \\ \nonumber
+    &2x+5y  \leq  100 \\ \nonumber
+    &3x+4y  \leq  80.  \\ \nonumber
+\end{align*}
+$$
 
+The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns)
+$$
+\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T   \begin{bmatrix} 1 & 0\\ 0 & 0  \end{bmatrix}  \begin{bmatrix} x \\ y \end{bmatrix}  + \begin{bmatrix}3\\ 4  \end{bmatrix}^T \begin{bmatrix}x \\ y  \end{bmatrix}.  
+$$
+
+Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation
+$$
+\begin{bmatrix} -1 & 0 \\ 0 & -1 \\ -1 & -3 \\ 2 & 5 \\ 3 & 4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} \preceq \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}.
+$$
+
+We have collapsed all the inequalities into a single matrix \( \boldsymbol{G} \). We see also that our matrix 
+$$
+\boldsymbol{P} =\begin{bmatrix} 1 & 0\\ 0 & 0  \end{bmatrix}
+$$
+
+is clearly positive semi-definite (all eigenvalues larger or equal zero). 
+Finally, the vector \( \boldsymbol{h} \) is defined as 
+$$
+\boldsymbol{h} = \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}.
+$$
+
+
    
+Since we don't have any equalities the matrix \( \boldsymbol{A} \) is set to zero
+The following code solves the equations for us
+
    
+
+
+
    # Import the necessary packages
+import numpy
+from cvxopt import matrix
+from cvxopt import solvers
+P = matrix(numpy.diag([1,0]), tc=’d’)
+q = matrix(numpy.array([3,4]), tc=’d’)
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
+h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+# Construct the QP, invoke solver
+sol = solvers.qp(P,q,G,h)
+# Extract optimal value and solution
+sol[’x’] 
+sol[’primal objective’]
+
    
 
    
 
    
 
@@ -284,7 +349,7 @@ With  the slack constants this leads to the additional constraint \( 0\leq \lamb
   
  • 22
    • 
   
  • 23
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs014.html b/doc/pub/week48/html/._week48-bs014.html
index 046ad400b..a74531df6 100644
--- a/doc/pub/week48/html/._week48-bs014.html
+++ b/doc/pub/week48/html/._week48-bs014.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,7 +258,22 @@ MathJax.Hub.Config({
 
 
 
-
    Summary of course 
    
+
    Back to the more realistic cases 
    
+
+
    
+We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the slack parameter \( C \) we have
+$$
+\frac{1}{2} \boldsymbol{\lambda}^T\begin{bmatrix} y_1y_1K(\boldsymbol{x}_1,\boldsymbol{x}_1) & y_1y_2K(\boldsymbol{x}_1,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_1,\boldsymbol{x}_n) \\
+y_2y_1K(\boldsymbol{x}_2,\boldsymbol{x}_1) & y_2y_2K(\boldsymbol{x}_2,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_2,\boldsymbol{x}_n) \\
+\dots & \dots & \dots & \dots & \dots \\
+\dots & \dots & \dots & \dots & \dots \\
+y_ny_1K(\boldsymbol{x}_n,\boldsymbol{x}_1) & y_ny_2K(\boldsymbol{x}_n\boldsymbol{x}_2) & \dots & \dots & y_ny_nK(\boldsymbol{x}_n,\boldsymbol{x}_n) \\
+\end{bmatrix}\boldsymbol{\lambda}-\mathbb{I}\boldsymbol{\lambda}, 
+$$
+
+subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and 
+\( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). 
+With  the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
 
 
    
 
    
@@ -269,7 +301,7 @@ MathJax.Hub.Config({
   
  • 23
    • 
   
  • 24
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs015.html b/doc/pub/week48/html/._week48-bs015.html
index 69f1ada7d..fa35d4a8c 100644
--- a/doc/pub/week48/html/._week48-bs015.html
+++ b/doc/pub/week48/html/._week48-bs015.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,8 +258,27 @@ MathJax.Hub.Config({
 
 
 
-
    What? Me worry? No final exam in this course! 
    
-



    
+
    Setting up the matrices and the problem 
    
+
+
    
+We have the general problem 
+$$
+\begin{align*}
+    &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
+    &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge  \boldsymbol{A}\boldsymbol{\lambda}=f.
+\end{align*}
+$$
+
+
+
      
+
    1.  With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
      2. 
+
    2.  The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
      3. 
+
    3.  The \( \boldsymbol{q} \) is zero.
      4. 
+
    4.  The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
      5. 
+
    5.  To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into
      6. 
+
    
+
+\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
 
 
    
 
    
@@ -270,7 +306,7 @@ MathJax.Hub.Config({
   
  • 24
    • 
   
  • 25
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs016.html b/doc/pub/week48/html/._week48-bs016.html
index 0cf9191df..c57531835 100644
--- a/doc/pub/week48/html/._week48-bs016.html
+++ b/doc/pub/week48/html/._week48-bs016.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,16 +258,47 @@ MathJax.Hub.Config({
 
 
 
-
    Topics we have covered this year 
    
+
    Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) 
    
 
 
    
-The course has two central parts
+We have two constraints, \( 0\le \lambda_i \) and \( \lambda_i \le C \). To do this we multiply the ones with the contraint
+\( \ge \) with \( -1 \) in order to get \( \le \). It means that the problem \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
+can be written as
+$$
+\begin{bmatrix} -1& 0 & 0 & \dots & 0 \\
+0& -1 & 0 & \dots & 0 \\
+0& 0 & -1 & \dots & 0 \\
+\dots& \dots & \dots  & \dots & \dots \\
+0& 0 & 0 & \dots & -1 \\
+ -& 0 & 0 & \dots & 0 \\
+0& 1 & 0 & \dots & 0 \\
+0& 0 & 1 & \dots & 0 \\
+\dots& \dots & \dots  & \dots & \dots \\
+0& 0 & 0 & \dots & 1 \\
+\end{bmatrix}\boldsymbol{\lambda}
+\begin{bmatrix} \lambda_1 \\
+\lambda_2 \\
+\lambda_3 \\
+\dots \\
+\lambda_n \\
+\end{bmatrix}\boldsymbol{\lambda}=
+\begin{bmatrix} 0 \\
+0 \\
+0 \\
+\dots \\
+0 \\
+C \\
+C \\
+C \\
+\dots \\
+C \\
+\end{bmatrix}\boldsymbol{\lambda}
+$$
 
-
      
-
    1.  Statistical analysis and optimization of data
      2. 
-
    2.  Machine learning
      3. 
-
    
+
    
+And then we are ready to go.
 
+
    
 
    
 
 
      
@@ -276,7 +324,7 @@ The course has two central parts
   
    • 25
      • 
   
    • 26
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs017.html b/doc/pub/week48/html/._week48-bs017.html
index 3b23be3e8..14398a4e8 100644
--- a/doc/pub/week48/html/._week48-bs017.html
+++ b/doc/pub/week48/html/._week48-bs017.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,21 +258,9 @@ MathJax.Hub.Config({
 
 
 
-
    Statistical analysis and optimization of data 
    
+
    Summary of course 
    
 
 
    
-The following topics  be covered
-
-
      
-
    1.  Basic concepts, expectation values, variance, covariance, correlation functions and errors;
      2. 
-
    2.  Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
      3. 
-
    3.  Central elements from linear algebra
      4. 
-
    4.  Gradient methods for data optimization
      5. 
-
    5.  Estimation of errors using cross-validation, bootstrapping and jackknife methods;
      6. 
-
    6.  Practical optimization using Singular-value decomposition and least squares for parameterizing data.
      7. 
-
    7.  Principal Component Analysis.
      8. 
-
    
-
 
    
 
 
      
@@ -281,7 +286,7 @@ The following topics  be covered
   
    • 26
      • 
   
    • 27
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs018.html b/doc/pub/week48/html/._week48-bs018.html
index ce0bce8c8..145557e7f 100644
--- a/doc/pub/week48/html/._week48-bs018.html
+++ b/doc/pub/week48/html/._week48-bs018.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,48 +258,10 @@ MathJax.Hub.Config({
 
 
 
-
    Machine learning 
    
+
    What? Me worry? No final exam in this course! 
    
+



    
 
 
    
-The following topics will be covered
-
-
      
-
    1.  Linear methods for regression and classification:
-
-
        
- 
      1.  Ordinary Least Squares
        2. 
- 
      2.  Ridge regression
        3. 
- 
      3.  Lasso regression
        4. 
- 
      4.  Logistic regression
        5. 
-
      
-
-
    2.  Neural networks and deep learning:
-
-
        
- 
      1.  Feed Forward Neural Networks
        2. 
- 
      2.  Convolutional Neural Networks
        3. 
- 
      3.  Recurrent Neural Networks
        4. 
-
      
-
-
    3.  Decisions trees and ensemble methods:
-
-
        
- 
      1.  Decision trees
        2. 
- 
      2.  Bagging and voting
        3. 
- 
      3.  Random forests
        4. 
- 
      4.  Boosting and gradient boosting
        5. 
-
      
-
-
    4.  Support vector machines
-
-
        
- 
      1.  Binary classification and multiclass classification
        2. 
- 
      2.  Kernel methods
        3. 
- 
      3.  Regression
        4. 
-
      
-
-
    
-
 
    
 
 
      
@@ -308,7 +287,7 @@ The following topics will be covered
   
    • 27
      • 
   
    • 28
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs019.html b/doc/pub/week48/html/._week48-bs019.html
index 75f486d99..87f38a2a6 100644
--- a/doc/pub/week48/html/._week48-bs019.html
+++ b/doc/pub/week48/html/._week48-bs019.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,29 +258,15 @@ MathJax.Hub.Config({
 
 
 
-
    Learning outcomes and overarching aims of this course 
    
+
    Topics we have covered this year 
    
 
 
    
-The course introduces a variety of central algorithms and methods
-essential for studies of data analysis and machine learning. The
-course is project based and through the various projects, normally
-three, you will be exposed to fundamental research problems
-in these fields, with the aim to reproduce state of the art scientific
-results. The students will learn to develop and structure large codes
-for studying these systems, get acquainted with computing facilities
-and learn to handle large scientific projects. A good scientific and
-ethical conduct is emphasized throughout the course. 
+The course has two central parts
 
-
      
-
    •  Understand linear methods for regression and classification;
      • 
-
    •  Learn about neural network;
      • 
-
    •  Learn about baggin, boosting and trees
      • 
-
    •  Support vector machines
      • 
-
    •  Learn about basic data analysis;
      • 
-
    •  Be capable of extending the acquired knowledge to other systems and cases;
      • 
-
    •  Have an understanding of central algorithms used in data analysis and machine learning;
      • 
-
    •  Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++.
      • 
-
    
+
      
+
    1.  Statistical analysis and optimization of data
      2. 
+
    2.  Machine learning
      3. 
+
    
 
 
    
 
@@ -290,7 +293,7 @@ ethical conduct is emphasized throughout the course.
   
  • 28
    • 
   
  • 29
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs020.html b/doc/pub/week48/html/._week48-bs020.html
index 480c1e964..b81880cac 100644
--- a/doc/pub/week48/html/._week48-bs020.html
+++ b/doc/pub/week48/html/._week48-bs020.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,21 +258,21 @@ MathJax.Hub.Config({
 
 
 
-
    Perspective on Machine Learning 
    
-
-
      
-
    1.  Rapidly emerging application area
      2. 
-
    2.  Experiment AND theory are evolving in many many fields. Still many low-hanging fruits.
      3. 
-
    3.  Requires education/retraining for more widespread adoption
      4. 
-
    4.  A lot of “word-of-mouth” development methods
      5. 
-
    
-
-Huge amounts of data sets require automation, classical analysis tools often inadequate. 
-High energy physics hit this wall in the 90’s.
-In 2009 single top quark production was determined via Boosted decision trees, Bayesian
-Neural Networks, etc.
+
    Statistical analysis and optimization of data 
    
 
 
    
+The following topics  be covered
+
+
      
+
    1.  Basic concepts, expectation values, variance, covariance, correlation functions and errors;
      2. 
+
    2.  Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
      3. 
+
    3.  Central elements from linear algebra
      4. 
+
    4.  Gradient methods for data optimization
      5. 
+
    5.  Estimation of errors using cross-validation, bootstrapping and jackknife methods;
      6. 
+
    6.  Practical optimization using Singular-value decomposition and least squares for parameterizing data.
      7. 
+
    7.  Principal Component Analysis.
      8. 
+
    
+
 
    
 
 
      
@@ -281,7 +298,7 @@ Neural Networks, etc.
   
    • 29
      • 
   
    • 30
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs021.html b/doc/pub/week48/html/._week48-bs021.html
index 37be0c4bc..8ca67668d 100644
--- a/doc/pub/week48/html/._week48-bs021.html
+++ b/doc/pub/week48/html/._week48-bs021.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,17 +258,46 @@ MathJax.Hub.Config({
 
 
 
-
    Machine Learning Research 
    
+
    Machine learning 
    
 
 
    
-Where to find recent results:
+The following topics will be covered
 
 
      
-
    1.  Conference proceedings, arXiv and blog posts!
      2. 
-
    2.  NIPS: Neural Information Processing Systems
      3. 
-
    3.  ICLR: International Conference on Learning Representations
      4. 
-
    4.  ICML: International Conference on Machine Learning
      5. 
-
    5.  Journal of Machine Learning Research
      6.  
+
    6.  Linear methods for regression and classification:
+
+
        
+ 
      1.  Ordinary Least Squares
        2. 
+ 
      2.  Ridge regression
        3. 
+ 
      3.  Lasso regression
        4. 
+ 
      4.  Logistic regression
        5. 
+
      
+
+
    7.  Neural networks and deep learning:
+
+
        
+ 
      1.  Feed Forward Neural Networks
        2. 
+ 
      2.  Convolutional Neural Networks
        3. 
+ 
      3.  Recurrent Neural Networks
        4. 
+
      
+
+
    8.  Decisions trees and ensemble methods:
+
+
        
+ 
      1.  Decision trees
        2. 
+ 
      2.  Bagging and voting
        3. 
+ 
      3.  Random forests
        4. 
+ 
      4.  Boosting and gradient boosting
        5. 
+
      
+
+
    9.  Support vector machines
+
+
        
+ 
      1.  Binary classification and multiclass classification
        2. 
+ 
      2.  Kernel methods
        3. 
+ 
      3.  Regression
        4. 
+
      
+
 
    
 
 
    
@@ -279,7 +325,7 @@ Where to find recent results:
   
  • 30
    • 
   
  • 31
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs022.html b/doc/pub/week48/html/._week48-bs022.html
index ecb712e1f..cba3affaf 100644
--- a/doc/pub/week48/html/._week48-bs022.html
+++ b/doc/pub/week48/html/._week48-bs022.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,15 +258,29 @@ MathJax.Hub.Config({
 
 
 
-
    Starting your Machine Learning Project  
    
+
    Learning outcomes and overarching aims of this course 
    
 
-
      
-
    1.  Identify problem type: classification, generation, regression
      2. 
-
    2.  Consider your data carefully
      3. 
-
    3.  Choose a simple model that fits 1. and 2.
      4. 
-
    4.  Consider your data carefully again… data representation
      5. 
-
    5.  Based on results, feedback loop to earliest possible point
      6. 
-
    
+
    
+The course introduces a variety of central algorithms and methods
+essential for studies of data analysis and machine learning. The
+course is project based and through the various projects, normally
+three, you will be exposed to fundamental research problems
+in these fields, with the aim to reproduce state of the art scientific
+results. The students will learn to develop and structure large codes
+for studying these systems, get acquainted with computing facilities
+and learn to handle large scientific projects. A good scientific and
+ethical conduct is emphasized throughout the course. 
+
+
      
+
    •  Understand linear methods for regression and classification;
      • 
+
    •  Learn about neural network;
      • 
+
    •  Learn about baggin, boosting and trees
      • 
+
    •  Support vector machines
      • 
+
    •  Learn about basic data analysis;
      • 
+
    •  Be capable of extending the acquired knowledge to other systems and cases;
      • 
+
    •  Have an understanding of central algorithms used in data analysis and machine learning;
      • 
+
    •  Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++.
      • 
+
    
 
 
    
 
@@ -276,7 +307,7 @@ MathJax.Hub.Config({
   
  • 31
    • 
   
  • 32
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs023.html b/doc/pub/week48/html/._week48-bs023.html
index 3e2dd5161..c2fe0e5aa 100644
--- a/doc/pub/week48/html/._week48-bs023.html
+++ b/doc/pub/week48/html/._week48-bs023.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,14 +258,21 @@ MathJax.Hub.Config({
 
 
 
-
    Choose a Model and Algorithm  
    
+
    Perspective on Machine Learning 
    
 
 
      
-
    1.  Supervised?
      2. 
-
    2.  Start with the simplest model that fits your problem
      3. 
-
    3.  Start with minimal processing of data
      4. 
+
    4.  Rapidly emerging application area
      5. 
+
    5.  Experiment AND theory are evolving in many many fields. Still many low-hanging fruits.
      6. 
+
    6.  Requires education/retraining for more widespread adoption
      7. 
+
    7.  A lot of “word-of-mouth” development methods
      8. 
 
    
 
+Huge amounts of data sets require automation, classical analysis tools often inadequate. 
+High energy physics hit this wall in the 90’s.
+In 2009 single top quark production was determined via Boosted decision trees, Bayesian
+Neural Networks, etc.
+
+
    
 
    
 
 
      
@@ -274,7 +298,7 @@ MathJax.Hub.Config({
   
    • 32
      • 
   
    • 33
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs024.html b/doc/pub/week48/html/._week48-bs024.html
index a124b4037..48ba59fa2 100644
--- a/doc/pub/week48/html/._week48-bs024.html
+++ b/doc/pub/week48/html/._week48-bs024.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,30 +258,17 @@ MathJax.Hub.Config({
 
 
 
-
    Preparing Your Data 
    
+
    Machine Learning Research 
    
+
+
    
+Where to find recent results:
 
 
      
-
    1.  Shuffle your data
      2. 
-
    2.  Mean center your data
      3. 
-
-
        
-  
      •  Why?
        • 
-
      
-
-
    3.  Normalize the variance
      4. 
-
-
        
-  
      •  Why?
        • 
-
      
-
-
    4.  Whitening
      5. 
-
-
        
-  
      •  Decorrelates data
        • 
-  
      •  Can be hit or miss
        • 
-
      
-
-
    5.  When to do train/test split?
      6. 
+
    6.  Conference proceedings, arXiv and blog posts!
      7. 
+
    7.  NIPS: Neural Information Processing Systems
      8. 
+
    8.  ICLR: International Conference on Learning Representations
      9. 
+
    9.  ICML: International Conference on Machine Learning
      10. 
+
    10.  Journal of Machine Learning Research
      11.  
 
    
 
 
    
@@ -292,7 +296,7 @@ MathJax.Hub.Config({
   
  • 33
    • 
   
  • 34
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs025.html b/doc/pub/week48/html/._week48-bs025.html
index 2db05de16..f9ddca4f1 100644
--- a/doc/pub/week48/html/._week48-bs025.html
+++ b/doc/pub/week48/html/._week48-bs025.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,23 +258,14 @@ MathJax.Hub.Config({
 
 
 
-
    Which Activation and Weights to Choose in Neural Networks 
    
+
    Starting your Machine Learning Project  
    
 
 
      
-
    1.  RELU? ELU?
      2. 
-
    2.  Sigmoid or Tanh?
      3. 
-
    3.  Set all weights to 0?
      4. 
-
-
        
-  
      •  Terrible idea
        • 
-
      
-
-
    4.  Set all weights to random values?
      5. 
-
-
        
-  
      •  Small random values
        • 
-
      
-
+
    5.  Identify problem type: classification, generation, regression
      6. 
+
    6.  Consider your data carefully
      7. 
+
    7.  Choose a simple model that fits 1. and 2.
      8. 
+
    8.  Consider your data carefully again… data representation
      9. 
+
    9.  Based on results, feedback loop to earliest possible point
      10. 
 
    
 
 
    
@@ -285,7 +293,7 @@ MathJax.Hub.Config({
   
  • 34
    • 
   
  • 35
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs026.html b/doc/pub/week48/html/._week48-bs026.html
index 587ce1df5..3e0c9a93b 100644
--- a/doc/pub/week48/html/._week48-bs026.html
+++ b/doc/pub/week48/html/._week48-bs026.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,27 +258,14 @@ MathJax.Hub.Config({
 
 
 
-
    Optimization Methods and Hyperparameters 
    
+
    Choose a Model and Algorithm  
    
 
 
      
-
    1.  Stochastic gradient descent
-
-
        
-
      1.  Stochastic gradient descent + momentum
        2. 
+
      2.  Supervised?
        3. 
+
      3.  Start with the simplest model that fits your problem
        4. 
+
      4.  Start with minimal processing of data
        5. 
 
      
 
-
    2.  State-of-the-art approaches:
      3. 
-
-
        
-  
      •  RMSProp
        • 
-  
      •  Adam
        • 
-
      
-
-
    
-
-Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifiers, depths of trees and many other. Need to explore a large set of hyperparameters and regularization methods.
-
-
    
 
    
 
 
      
@@ -287,7 +291,7 @@ Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifie
   
    • 35
      • 
   
    • 36
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs027.html b/doc/pub/week48/html/._week48-bs027.html
index 7470ed784..1f1b86b9d 100644
--- a/doc/pub/week48/html/._week48-bs027.html
+++ b/doc/pub/week48/html/._week48-bs027.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,15 +258,30 @@ MathJax.Hub.Config({
 
 
 
-
    Resampling 
    
-
-
    
-When do we resample?
+
    Preparing Your Data 
    
 
 
      
-
    1.  Bootstrap
      2. 
-
    2.  Cross-validation
      3. 
-
    3.  Jackknife and many other
      4. 
+
    4.  Shuffle your data
      5. 
+
    5.  Mean center your data
      6. 
+
+
        
+  
      •  Why?
        • 
+
      
+
+
    6.  Normalize the variance
      7. 
+
+
        
+  
      •  Why?
        • 
+
      
+
+
    7.  Whitening
      8. 
+
+
        
+  
      •  Decorrelates data
        • 
+  
      •  Can be hit or miss
        • 
+
      
+
+
    8.  When to do train/test split?
      9. 
 
    
 
 
    
@@ -277,7 +309,7 @@ When do we resample?
   
  • 36
    • 
   
  • 37
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs028.html b/doc/pub/week48/html/._week48-bs028.html
index db0f4edcb..6971f58e6 100644
--- a/doc/pub/week48/html/._week48-bs028.html
+++ b/doc/pub/week48/html/._week48-bs028.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,20 +258,23 @@ MathJax.Hub.Config({
 
 
 
-
    Other courses on Data science and Machine Learning  at UiO 
    
-
-
    
-The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/  gives an excellent overview of courses on Machine learning at UiO.
+
    Which Activation and Weights to Choose in Neural Networks 
    
 
 
      
-
    1.  STK2100 Machine learning and statistical methods for prediction and classification.
      2.  
-
    2.  IN3050/IN4050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
      3.  
-
    3.  STK-INF3000/4000 Selected Topics in Data Science. The course provides insight into selected contemporary relevant topics within Data Science.
      4.  
-
    4.  IN4080 Natural Language Processing. Probabilistic and machine learning techniques applied to natural language processing.
      5.  
-
    5.  STK-IN4300 – Statistical learning methods in Data Science. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
      6. 
-
    6.  IN-STK5000  Adaptive Methods for Data-Based Decision Making. Methods for adaptive collection and processing of data based on machine learning techniques.
      7.  
-
    7.  IN5400/INF5860 – Machine Learning for Image Analysis. An introduction to deep learning with particular emphasis on applications within Image analysis, but useful for other application areas too.
      8. 
-
    8.  TEK5040 – Dyp læring for autonome systemer. The course addresses advanced algorithms and architectures for deep learning with neural networks. The course provides an introduction to how deep-learning techniques can be used in the construction of key parts of advanced autonomous systems that exist in physical environments and cyber environments.
      9. 
+
    9.  RELU? ELU?
      10. 
+
    10.  Sigmoid or Tanh?
      11. 
+
    11.  Set all weights to 0?
      12. 
+
+
        
+  
      •  Terrible idea
        • 
+
      
+
+
    12.  Set all weights to random values?
      13. 
+
+
        
+  
      •  Small random values
        • 
+
      
+
 
    
 
 
    
@@ -282,7 +302,7 @@ The link here 37
   
  • 38
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs029.html b/doc/pub/week48/html/._week48-bs029.html
index cc7c77f31..72636ddc5 100644
--- a/doc/pub/week48/html/._week48-bs029.html
+++ b/doc/pub/week48/html/._week48-bs029.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,13 +258,27 @@ MathJax.Hub.Config({
 
 
 
-
    Additional courses of interest 
    
+
    Optimization Methods and Hyperparameters 
    
 
 
      
-
    1.  STK4051 Computational Statistics
      2. 
-
    2.  STK4021 Applied Bayesian Analysis and Numerical Methods
      3. 
+
    3.  Stochastic gradient descent
+
+
        
+
      1.  Stochastic gradient descent + momentum
        2. 
 
      
 
+
    4.  State-of-the-art approaches:
      5. 
+
+
        
+  
      •  RMSProp
        • 
+  
      •  Adam
        • 
+
      
+
+
    
+
+Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifiers, depths of trees and many other. Need to explore a large set of hyperparameters and regularization methods.
+
+
    
 
    
 
 
      
@@ -273,7 +304,7 @@ MathJax.Hub.Config({
   
    • 38
      • 
   
    • 39
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs030.html b/doc/pub/week48/html/._week48-bs030.html
index 57965bcae..858b10775 100644
--- a/doc/pub/week48/html/._week48-bs030.html
+++ b/doc/pub/week48/html/._week48-bs030.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,25 +258,15 @@ MathJax.Hub.Config({
 
 
 
-
    What's the future like?  
    
+
    Resampling 
    
 
 
    
-Based on multi-layer nonlinear neural networks, deep learning can
-learn directly from raw data, automatically extract and abstract
-features from layer to layer, and then achieve the goal of regression,
-classification, or ranking. Deep learning has made breakthroughs in
-computer vision, speech processing and natural language, and reached
-or even surpassed human level. The success of deep learning is mainly
-due to the three factors: big data, big model, and big computing.
-
-
    
-In the past few decades, many different architectures of deep neural
-networks have been proposed, such as
+When do we resample?
 
 
      
-
    1.  Convolutional neural networks, which are mostly used in image and video data processing, and have also been applied to sequential data such as text processing;
      2. 
-
    2.  Recurrent neural networks, which can process sequential data of variable length and have been widely used in natural language understanding and speech processing;
      3. 
-
    3.  Encoder-decoder framework, which is mostly used for image or sequence generation, such as machine translation, text summarization, and image captioning.
      4. 
+
    4.  Bootstrap
      5. 
+
    5.  Cross-validation
      6. 
+
    6.  Jackknife and many other
      7. 
 
    
 
 
    
@@ -287,7 +294,7 @@ networks have been proposed, such as
   
  • 39
    • 
   
  • 40
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs031.html b/doc/pub/week48/html/._week48-bs031.html
index 048ac99f9..6c7b4960d 100644
--- a/doc/pub/week48/html/._week48-bs031.html
+++ b/doc/pub/week48/html/._week48-bs031.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,35 +258,22 @@ MathJax.Hub.Config({
 
 
 
-
    Types of Machine Learning, a repetition 
    
+
    Other courses on Data science and Machine Learning  at UiO 
    
 
 
    
-
    
-
    
-
     
-The approaches to machine learning are many, but are often split into two main categories. 
-In supervised learning we know the answer to a problem,
-and let the computer deduce the logic behind it. On the other hand, unsupervised learning
-is a method for finding patterns and relationship in data sets without any prior knowledge of the system.
-Some authours also operate with a third category, namely reinforcement learning. This is a paradigm 
-of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, 
-solely from rewards and punishment.
+The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/  gives an excellent overview of courses on Machine learning at UiO.
 
-
    
-Another way to categorize machine learning tasks is to consider the desired output of a system.
-Some of the most common tasks are:
+
      
+
    1.  STK2100 Machine learning and statistical methods for prediction and classification.
      2.  
+
    2.  IN3050/IN4050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
      3.  
+
    3.  STK-INF3000/4000 Selected Topics in Data Science. The course provides insight into selected contemporary relevant topics within Data Science.
      4.  
+
    4.  IN4080 Natural Language Processing. Probabilistic and machine learning techniques applied to natural language processing.
      5.  
+
    5.  STK-IN4300 – Statistical learning methods in Data Science. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
      6. 
+
    6.  IN-STK5000  Adaptive Methods for Data-Based Decision Making. Methods for adaptive collection and processing of data based on machine learning techniques.
      7.  
+
    7.  IN5400/INF5860 – Machine Learning for Image Analysis. An introduction to deep learning with particular emphasis on applications within Image analysis, but useful for other application areas too.
      8. 
+
    8.  TEK5040 – Dyp læring for autonome systemer. The course addresses advanced algorithms and architectures for deep learning with neural networks. The course provides an introduction to how deep-learning techniques can be used in the construction of key parts of advanced autonomous systems that exist in physical environments and cyber environments.
      9. 
+
    
 
-
      
-  
    •  Classification: Outputs are divided into two or more classes. The goal is to   produce a model that assigns inputs into one of these classes. An example is to identify  digits based on pictures of hand-written ones. Classification is typically supervised learning.
      • 
-  
    •  Regression: Finding a functional relationship between an input data set and a reference data set.   The goal is to construct a function that maps input data to continuous output values.
      • 
-  
    •  Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand.  It is thus a form of unsupervised learning.
      • 
-  
    •  Other unsupervised learning algortihms like Boltzmann machines
      • 
-
    
-
    
-
    
-
-
-
    
 
    
 
 
      
@@ -295,7 +299,7 @@ Some of the most common tasks are:
   
    • 40
      • 
   
    • 41
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs032.html b/doc/pub/week48/html/._week48-bs032.html
index fa11355c1..dd61f7971 100644
--- a/doc/pub/week48/html/._week48-bs032.html
+++ b/doc/pub/week48/html/._week48-bs032.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,19 +258,13 @@ MathJax.Hub.Config({
 
 
 
-
    Why Boltzmann machines? 
    
+
    Additional courses of interest 
    
 
-
    
-What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. 
-One of the major reasons is that they can be stacked layer-wise to build deep neural networks that capture complicated statistics.
+
      
+
    1.  STK4051 Computational Statistics
      2. 
+
    2.  STK4021 Applied Bayesian Analysis and Numerical Methods
      3. 
+
    
 
-
    
-The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
-
-
    
-Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
-
-
    
 
    
 
 
      
@@ -279,7 +290,7 @@ Furthermore, they have been used to solve complicated 41
   
    • 42
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs033.html b/doc/pub/week48/html/._week48-bs033.html
index 3209bf89f..4588ef13d 100644
--- a/doc/pub/week48/html/._week48-bs033.html
+++ b/doc/pub/week48/html/._week48-bs033.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,23 +258,27 @@ MathJax.Hub.Config({
 
 
 
-
    Boltzmann Machines 
    
+
    What's the future like?  
    
 
 
    
-Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? 
+Based on multi-layer nonlinear neural networks, deep learning can
+learn directly from raw data, automatically extract and abstract
+features from layer to layer, and then achieve the goal of regression,
+classification, or ranking. Deep learning has made breakthroughs in
+computer vision, speech processing and natural language, and reached
+or even surpassed human level. The success of deep learning is mainly
+due to the three factors: big data, big model, and big computing.
 
-
      
-
    •  Discriminitave methods have several limitations: They are mainly supervised learning methods, thus requiring labeled data. And there are tasks they cannot accomplish, like drawing new examples from an unknown probability distribution.
      • 
-
    •  A generative model can learn to represent and sample from a probability distribution. The core idea is to learn a parametric model of the probability distribution from which the training data was drawn. As an example
+
      
+In the past few decades, many different architectures of deep neural
+networks have been proposed, such as
 
-
        
- 
      1.  A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.
        2. 
- 
      2.  Generate a sample of an ordered or disordered phase, having been given samples of such phases.
        3. 
- 
      3.  Model the trial function for Monte Carlo calculations.
        4. 
+
          
+
        1.  Convolutional neural networks, which are mostly used in image and video data processing, and have also been applied to sequential data such as text processing;
          2. 
+
        2.  Recurrent neural networks, which can process sequential data of variable length and have been widely used in natural language understanding and speech processing;
          3. 
+
        3.  Encoder-decoder framework, which is mostly used for image or sequence generation, such as machine translation, text summarization, and image captioning.
          4. 
 
        
 
-
    
-
 
    
 
 
      
@@ -283,7 +304,7 @@ Why use a generative model rather than the more well known discriminative deep n
   
    • 42
      • 
   
    • 43
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs034.html b/doc/pub/week48/html/._week48-bs034.html
index c8486fe74..1ef738819 100644
--- a/doc/pub/week48/html/._week48-bs034.html
+++ b/doc/pub/week48/html/._week48-bs034.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,15 +258,33 @@ MathJax.Hub.Config({
 
 
 
-
    Some similarities and differences from DNNs 
    
+
    Types of Machine Learning, a repetition 
    
 
-
      
-
    1.  Both use gradient-descent based learning procedures for minimizing cost functions
      2. 
-
    2.  Energy based models don't use backpropagation and automatic differentiation for computing gradients, instead turning to Markov Chain Monte Carlo methods.
      3. 
-
    3.  DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.
      4. 
-
    
+
    
+
    
+
    
+
     
+The approaches to machine learning are many, but are often split into two main categories. 
+In supervised learning we know the answer to a problem,
+and let the computer deduce the logic behind it. On the other hand, unsupervised learning
+is a method for finding patterns and relationship in data sets without any prior knowledge of the system.
+Some authours also operate with a third category, namely reinforcement learning. This is a paradigm 
+of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, 
+solely from rewards and punishment.
+
+
    
+Another way to categorize machine learning tasks is to consider the desired output of a system.
+Some of the most common tasks are:
+
+
      
+  
    •  Classification: Outputs are divided into two or more classes. The goal is to   produce a model that assigns inputs into one of these classes. An example is to identify  digits based on pictures of hand-written ones. Classification is typically supervised learning.
      • 
+  
    •  Regression: Finding a functional relationship between an input data set and a reference data set.   The goal is to construct a function that maps input data to continuous output values.
      • 
+  
    •  Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand.  It is thus a form of unsupervised learning.
      • 
+  
    •  Other unsupervised learning algortihms like Boltzmann machines
      • 
+
    
+
    
+
    
 
-History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
 
 
    
 
    
@@ -277,7 +312,7 @@ History: The RBM was developed by amongst others 43
   
  • 44
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs035.html b/doc/pub/week48/html/._week48-bs035.html
index 443b28756..d9ebdf11d 100644
--- a/doc/pub/week48/html/._week48-bs035.html
+++ b/doc/pub/week48/html/._week48-bs035.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,37 +258,17 @@ MathJax.Hub.Config({
 
 
 
-
    Boltzmann machines (BM) 
    
+
    Why Boltzmann machines? 
    
 
 
    
-
    
-
    
-
     
-A BM is what we would call an undirected probabilistic graphical model
-with stochastic continuous or discrete units.
-
    
-
    
+What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. 
+One of the major reasons is that they can be stacked layer-wise to build deep neural networks that capture complicated statistics.
 
-
    
-
    
-
     
-It is interpreted as a stochastic recurrent neural network where the
-state of each unit(neurons/nodes) depends on the units it is connected
-to. The weights in the network represent thus the strength of the
-interaction between various units/nodes.
-
    
-
    
-
-
    
-
    
-
     
-It turns into a Hopfield network if we choose deterministic rather
-than stochastic units. In contrast to a Hopfield network, a BM is a
-so-called generative model. It allows us to generate new samples from
-the learned distribution.
-
    
-
    
+
    
+The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
 
+
    
+Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
 
 
    
 
    
@@ -299,7 +296,7 @@ the learned distribution.
   
  • 44
    • 
   
  • 45
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs036.html b/doc/pub/week48/html/._week48-bs036.html
index f37996fc8..25b5111ae 100644
--- a/doc/pub/week48/html/._week48-bs036.html
+++ b/doc/pub/week48/html/._week48-bs036.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,40 +258,23 @@ MathJax.Hub.Config({
 
 
 
-
    A standard BM setup 
    
+
    Boltzmann Machines 
    
 
 
    
-
    
-
    
-
     
-A standard BM network is divided into a set of observable and visible units \( \hat{x} \) and a set of unknown hidden units/nodes \( \hat{h} \).
-
    
-
    
+Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? 
 
+
      
+
    •  Discriminitave methods have several limitations: They are mainly supervised learning methods, thus requiring labeled data. And there are tasks they cannot accomplish, like drawing new examples from an unknown probability distribution.
      • 
+
    •  A generative model can learn to represent and sample from a probability distribution. The core idea is to learn a parametric model of the probability distribution from which the training data was drawn. As an example
 
-
      
-
      
-
      
-
       
-Additionally there can be bias nodes for the hidden and visible layers. These biases are normally set to \( 1 \).
-
      
-
      
+
        
+ 
      1.  A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.
        2. 
+ 
      2.  Generate a sample of an ordered or disordered phase, having been given samples of such phases.
        3. 
+ 
      3.  Model the trial function for Monte Carlo calculations.
        4. 
+
      
 
+
    
 
-
    
-
    
-
    
-
     
-BMs are stackable, meaning they cwe can train a BM which serves as input to another BM. We can construct deep networks for learning complex PDFs. The layers can be trained one after another, a feature which makes them popular in deep learning
-
    
-
    
-
-
-
    
-However, they are often hard to train. This leads to the introduction of so-called restricted BMs, or RBMS.
-Here we take away all lateral connections between nodes in the visible layer as well as connections between nodes in the hidden layer. The network is illustrated in the figure below.
-
-
    
 
    
 
 
      
@@ -300,7 +300,7 @@ Here we take away all lateral connections between nodes in the visible layer as
   
    • 45
      • 
   
    • 46
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs037.html b/doc/pub/week48/html/._week48-bs037.html
index c743b60f0..7e8408a48 100644
--- a/doc/pub/week48/html/._week48-bs037.html
+++ b/doc/pub/week48/html/._week48-bs037.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,10 +258,15 @@ MathJax.Hub.Config({
 
 
 
-
    The structure of the RBM network 
    
+
    Some similarities and differences from DNNs 
    
 
-
    
-



    
+
      
+
    1.  Both use gradient-descent based learning procedures for minimizing cost functions
      2. 
+
    2.  Energy based models don't use backpropagation and automatic differentiation for computing gradients, instead turning to Markov Chain Monte Carlo methods.
      3. 
+
    3.  DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.
      4. 
+
    
+
+History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
 
 
    
 
    
@@ -272,7 +294,7 @@ MathJax.Hub.Config({
   
  • 46
    • 
   
  • 47
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs038.html b/doc/pub/week48/html/._week48-bs038.html
index 753385a79..d6f6f39aa 100644
--- a/doc/pub/week48/html/._week48-bs038.html
+++ b/doc/pub/week48/html/._week48-bs038.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,16 +258,39 @@ MathJax.Hub.Config({
 
 
 
-
    The network 
    
+
    Boltzmann machines (BM) 
    
 
 
    
-The network layers:
+
    
+
    
+
     
+A BM is what we would call an undirected probabilistic graphical model
+with stochastic continuous or discrete units.
+
    
+
    
 
-
      
- 
    1.  A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.
      2. 
- 
    2.  The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".
      3. 
-
    
+
    
+
    
+
     
+It is interpreted as a stochastic recurrent neural network where the
+state of each unit(neurons/nodes) depends on the units it is connected
+to. The weights in the network represent thus the strength of the
+interaction between various units/nodes.
+
    
+
    
 
+
    
+
    
+
     
+It turns into a Hopfield network if we choose deterministic rather
+than stochastic units. In contrast to a Hopfield network, a BM is a
+so-called generative model. It allows us to generate new samples from
+the learned distribution.
+
    
+
    
+
+
+
    
 
    
 
 
      
@@ -276,7 +316,7 @@ MathJax.Hub.Config({
   
    • 47
      • 
   
    • 48
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs039.html b/doc/pub/week48/html/._week48-bs039.html
index c2c0afe79..881a65fc4 100644
--- a/doc/pub/week48/html/._week48-bs039.html
+++ b/doc/pub/week48/html/._week48-bs039.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,25 +258,40 @@ MathJax.Hub.Config({
 
 
 
-
    Goals 
    
+
    A standard BM setup 
    
 
 
    
-The goal of the hidden layer is to increase the model's expressive
-power. We encode complex interactions between visible variables by
-introducing additional, hidden variables that interact with visible
-degrees of freedom in a simple manner, yet still reproduce the complex
-correlations between visible degrees in the data once marginalized
-over (integrated out).
+
    
+
    
+
     
+A standard BM network is divided into a set of observable and visible units \( \hat{x} \) and a set of unknown hidden units/nodes \( \hat{h} \).
+
    
+
    
+
 
 
    
-The network parameters, to be optimized/learned:
+
    
+
    
+
     
+Additionally there can be bias nodes for the hidden and visible layers. These biases are normally set to \( 1 \).
+
    
+
    
 
-
      
- 
    1.  \( \mathbf{a} \) represents the visible bias, a vector of same length as \( \mathbf{x} \).
      2. 
- 
    2.  \( \mathbf{b} \) represents the hidden bias, a vector of same lenght as \( \mathbf{h} \).
      3. 
- 
    3.  \( W \) represents the interaction weights, a matrix of size \( M\times N \).
      4. 
-
    
 
+
    
+
    
+
    
+
     
+BMs are stackable, meaning they cwe can train a BM which serves as input to another BM. We can construct deep networks for learning complex PDFs. The layers can be trained one after another, a feature which makes them popular in deep learning
+
    
+
    
+
+
+
    
+However, they are often hard to train. This leads to the introduction of so-called restricted BMs, or RBMS.
+Here we take away all lateral connections between nodes in the visible layer as well as connections between nodes in the hidden layer. The network is illustrated in the figure below.
+
+
    
 
    
 
 
      
@@ -285,7 +317,7 @@ over (integrated out).
   
    • 48
      • 
   
    • 49
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs040.html b/doc/pub/week48/html/._week48-bs040.html
index bbb61cd38..8c2d1c2b7 100644
--- a/doc/pub/week48/html/._week48-bs040.html
+++ b/doc/pub/week48/html/._week48-bs040.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,26 +258,10 @@ MathJax.Hub.Config({
 
 
 
-
    Joint distribution 
    
+
    The structure of the RBM network 
    
 
 
    
-The restricted Boltzmann machine is described by a Bolztmann distribution
-$$
-\begin{align}
-	P_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})},
-\tag{1}
-\end{align}
-$$
-
-where \( Z \) is the normalization constant or partition function, defined as 
-$$
-\begin{align}
-	Z = \int \int e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})} d\mathbf{x} d\mathbf{h}.
-\tag{2}
-\end{align}
-$$
-
-It is common to ignore \( T_0 \) by setting it to one.
+



    
 
 
    
 
    
@@ -288,7 +289,7 @@ It is common to ignore \( T_0 \) by setting it to one.
   
  • 49
    • 
   
  • 50
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs041.html b/doc/pub/week48/html/._week48-bs041.html
index 66fc855c7..cc1b2be9f 100644
--- a/doc/pub/week48/html/._week48-bs041.html
+++ b/doc/pub/week48/html/._week48-bs041.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,32 +258,16 @@ MathJax.Hub.Config({
 
 
 
-
    Network Elements, the energy function  
    
+
    The network 
    
 
 
    
-The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a
-configuration (pair of vectors) \( (\mathbf{x}, \mathbf{h}) \). The lower
-the energy of a configuration, the higher the probability of it. This
-function also depends on the parameters \( \mathbf{a} \), \( \mathbf{b} \) and
-\( W \). Thus, when we adjust them during the learning procedure, we are
-adjusting the energy function to best fit our problem.
+The network layers:
 
-
    
-An expression for the energy function is
-$$
-E(\hat{x},\hat{h}) = -\sum_{ia}^{NA}b_i^a \alpha_i^a(x_i)-\sum_{jd}^{MD}c_j^d \beta_j^d(h_j)-\sum_{ijad}^{NAMD}b_i^a \alpha_i^a(x_i)c_j^d \beta_j^d(h_j)w_{ij}^{ad}.
-$$
+
      
+ 
    1.  A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.
      2. 
+ 
    2.  The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".
      3. 
+
    
 
-
    
-Here \( \beta_j^d(h_j) \) and \( \alpha_i^a(x_j) \) are so-called transfer functions that map a given input value to a desired feature value. The labels \( a \) and \( d \) denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. Note that there is no connection between nodes in a layer.
-
-
    
-The quantities \( b \) and \( c \) can be interpreted as the visible and hidden biases, respectively.
-
-
    
-The connection between the nodes in the two layers is given by the weights \( w_{ij} \).
-
-
    
 
    
 
 
      
@@ -292,7 +293,7 @@ The connection between the nodes in the two layers is given by the weights \( w_
   
    • 50
      • 
   
    • 51
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs042.html b/doc/pub/week48/html/._week48-bs042.html
index 8e07eff34..f2e0d37cf 100644
--- a/doc/pub/week48/html/._week48-bs042.html
+++ b/doc/pub/week48/html/._week48-bs042.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,44 +258,25 @@ MathJax.Hub.Config({
 
 
 
-
    Defining different types of RBMs 
    
-There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function \( E(\mathbf{x},\mathbf{h}) \).
+
    Goals 
    
 
 
    
-
    
-
    
-
     
+The goal of the hidden layer is to increase the model's expressive
+power. We encode complex interactions between visible variables by
+introducing additional, hidden variables that interact with visible
+degrees of freedom in a simple manner, yet still reproduce the complex
+correlations between visible degrees in the data once marginalized
+over (integrated out).
 
 
    
-RBMs were first developed using binary units in both the visible and hidden layer. The corresponding energy function is defined as follows:
-$$
-\begin{align}
-	E(\mathbf{x}, \mathbf{h}) = - \sum_i^M x_i a_i- \sum_j^N b_j h_j - \sum_{i,j}^{M,N} x_i w_{ij} h_j,
-\tag{3}
-\end{align}
-$$
+The network parameters, to be optimized/learned:
 
-where the binary values taken on by the nodes are most commonly 0 and 1.
-
    
-
    
+
      
+ 
    1.  \( \mathbf{a} \) represents the visible bias, a vector of same length as \( \mathbf{x} \).
      2. 
+ 
    2.  \( \mathbf{b} \) represents the hidden bias, a vector of same lenght as \( \mathbf{h} \).
      3. 
+ 
    3.  \( W \) represents the interaction weights, a matrix of size \( M\times N \).
      4. 
+
    
 
-
    
-
    
-
     
-
-
    
-Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary:
-$$
-\begin{align}
-	E(\mathbf{x}, \mathbf{h}) = \sum_i^M \frac{(x_i - a_i)^2}{2\sigma_i^2} - \sum_j^N b_j h_j - \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma_i^2}. 
-\tag{4}
-\end{align}
-$$
-
    
-
    
-
-
-
    
 
    
 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs043.html b/doc/pub/week48/html/._week48-bs043.html
index 9a9501622..85f216937 100644
--- a/doc/pub/week48/html/._week48-bs043.html
+++ b/doc/pub/week48/html/._week48-bs043.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,22 +258,28 @@ MathJax.Hub.Config({
 
 
 
-
    More about RBMs 
    
+
    Joint distribution 
    
 
-
      
-
    1.  Useful when we model continuous data (i.e., we wish \( \mathbf{x} \) to be continuous)
      2. 
-
    2.  Requires a smaller learning rate, since there's no upper bound to the value a component might take in the reconstruction
      3. 
-
    
+
    
+The restricted Boltzmann machine is described by a Bolztmann distribution
+$$
+\begin{align}
+	P_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})},
+\tag{1}
+\end{align}
+$$
 
-Other types of units include:
+where \( Z \) is the normalization constant or partition function, defined as 
+$$
+\begin{align}
+	Z = \int \int e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})} d\mathbf{x} d\mathbf{h}.
+\tag{2}
+\end{align}
+$$
 
-
      
-
    1.  Softmax and multinomial units
      2. 
-
    2.  Gaussian visible and hidden units
      3. 
-
    3.  Binomial units
      4. 
-
    4.  Rectified linear units
      5. 
-
    
+It is common to ignore \( T_0 \) by setting it to one.
 
+
    
 
    
 
 
      
@@ -282,7 +305,7 @@ Other types of units include:
   
    • 52
      • 
   
    • 53
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs044.html b/doc/pub/week48/html/._week48-bs044.html
index 4a92abe90..c975ff091 100644
--- a/doc/pub/week48/html/._week48-bs044.html
+++ b/doc/pub/week48/html/._week48-bs044.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,40 +258,30 @@ MathJax.Hub.Config({
 
 
 
-
    Autoencoders: Overarching view 
    
+
    Network Elements, the energy function  
    
 
 
    
-Autoencoders are artificial neural networks capable of learning
-efficient representations of the input data (these representations are called codings)  without
-any supervision (i.e., the training set is unlabeled). These codings
-typically have a much lower dimensionality than the input data, making
-autoencoders useful for dimensionality reduction.
+The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a
+configuration (pair of vectors) \( (\mathbf{x}, \mathbf{h}) \). The lower
+the energy of a configuration, the higher the probability of it. This
+function also depends on the parameters \( \mathbf{a} \), \( \mathbf{b} \) and
+\( W \). Thus, when we adjust them during the learning procedure, we are
+adjusting the energy function to best fit our problem.
 
 
    
-More importantly, autoencoders act as powerful feature detectors, and
-they can be used for unsupervised pretraining of deep neural networks.
+An expression for the energy function is
+$$
+E(\hat{x},\hat{h}) = -\sum_{ia}^{NA}b_i^a \alpha_i^a(x_i)-\sum_{jd}^{MD}c_j^d \beta_j^d(h_j)-\sum_{ijad}^{NAMD}b_i^a \alpha_i^a(x_i)c_j^d \beta_j^d(h_j)w_{ij}^{ad}.
+$$
 
 
    
-Lastly, they are capable of randomly generating new data that looks
-very similar to the training data; this is called a generative
-model. For example, you could train an autoencoder on pictures of
-faces, and it would then be able to generate new faces.  Surprisingly,
-autoencoders work by simply learning to copy their inputs to their
-outputs. This may sound like a trivial task, but we will see that
-constraining the network in various ways can make it rather
-difficult. For example, you can limit the size of the internal
-representation, or you can add noise to the inputs and train the
-network to recover the original inputs. These constraints prevent the
-autoencoder from trivially copying the inputs directly to the outputs,
-which forces it to learn efficient ways of representing the data. In
-short, the codings are byproducts of the autoencoder’s attempt to
-learn the identity function under some constraints.
+Here \( \beta_j^d(h_j) \) and \( \alpha_i^a(x_j) \) are so-called transfer functions that map a given input value to a desired feature value. The labels \( a \) and \( d \) denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. Note that there is no connection between nodes in a layer.
 
 
    
-Video on autoencoders
+The quantities \( b \) and \( c \) can be interpreted as the visible and hidden biases, respectively.
 
 
    
-See also A. Geron's textbook, chapter 15.
+The connection between the nodes in the two layers is given by the weights \( w_{ij} \).
 
 
    
 
    
@@ -302,7 +309,7 @@ See also A. Geron's textbook, chapter 15.
   
  • 53
    • 
   
  • 54
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs045.html b/doc/pub/week48/html/._week48-bs045.html
index ca9ab008b..6ebbd1fd0 100644
--- a/doc/pub/week48/html/._week48-bs045.html
+++ b/doc/pub/week48/html/._week48-bs045.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,24 +258,42 @@ MathJax.Hub.Config({
 
 
 
-
    Bayesian Machine Learning 
    
+
    Defining different types of RBMs 
    
+There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function \( E(\mathbf{x},\mathbf{h}) \).
 
 
    
-This is an important topic if we aim at extracting a probability
-distribution. This gives us also a confidence interval and error
-estimates.
+
    
+
    
+
     
 
 
    
-Bayesian machine learning allows us to encode our prior beliefs about
-what those models should look like, independent of what the data tells
-us. This is especially useful when we don’t have a ton of data to
-confidently learn our model.
+RBMs were first developed using binary units in both the visible and hidden layer. The corresponding energy function is defined as follows:
+$$
+\begin{align}
+	E(\mathbf{x}, \mathbf{h}) = - \sum_i^M x_i a_i- \sum_j^N b_j h_j - \sum_{i,j}^{M,N} x_i w_{ij} h_j,
+\tag{3}
+\end{align}
+$$
+
+where the binary values taken on by the nodes are most commonly 0 and 1.
+
    
+
    
+
+
    
+
    
+
     
 
 
    
-Video on Bayesian deep learning
+Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary:
+$$
+\begin{align}
+	E(\mathbf{x}, \mathbf{h}) = \sum_i^M \frac{(x_i - a_i)^2}{2\sigma_i^2} - \sum_j^N b_j h_j - \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma_i^2}. 
+\tag{4}
+\end{align}
+$$
+
    
+
    
 
-
    
-See also the slides here.
 
 
    
 
    
@@ -286,7 +321,7 @@ See also the 54
   
  • 55
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs046.html b/doc/pub/week48/html/._week48-bs046.html
index 1c2d69256..b8fcad8e7 100644
--- a/doc/pub/week48/html/._week48-bs046.html
+++ b/doc/pub/week48/html/._week48-bs046.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,38 +258,22 @@ MathJax.Hub.Config({
 
 
 
-
    Reinforcement Learning 
    
+
    More about RBMs 
    
 
-
    
-Reinforcement Learning (RL) is one of the most exciting fields of
-Machine Learning today, and also one of the oldest. It has been around
-since the 1950s, producing many interesting applications over the
-years.
+
      
+
    1.  Useful when we model continuous data (i.e., we wish \( \mathbf{x} \) to be continuous)
      2. 
+
    2.  Requires a smaller learning rate, since there's no upper bound to the value a component might take in the reconstruction
      3. 
+
    
 
-
    
-It studies
-how agents take actions based on trial and error, so as to maximize
-some notion of cumulative reward in a dynamic system or
-environment. Due to its generality, the problem has also been studied
-in many other disciplines, such as game theory, control theory,
-operations research, information theory, multi-agent systems, swarm
-intelligence, statistics, and genetic algorithms.
+Other types of units include:
 
-
    
-In March 2016, AlphaGo, a computer program that plays the board game
-Go, beat Lee Sedol in a five-game match. This was the first time a
-computer Go program had beaten a 9-dan (highest rank) professional
-without handicaps. AlphaGo is based on deep convolutional neural
-networks and reinforcement learning. AlphaGo’s victory was a major
-milestone in artificial intelligence and it has also made
-reinforcement learning a hot research area in the field of machine
-learning.
+
      
+
    1.  Softmax and multinomial units
      2. 
+
    2.  Gaussian visible and hidden units
      3. 
+
    3.  Binomial units
      4. 
+
    4.  Rectified linear units
      5. 
+
    
 
-
    
-Lecture on Reinforcement Learning.
-
-
    
-See also A. Geron's textbook, chapter 16.
 
    
 
 
      
@@ -298,7 +299,7 @@ See also A. Geron's textbook, chapter 16.
   
    • 55
      • 
   
    • 56
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs047.html b/doc/pub/week48/html/._week48-bs047.html
index bf4b5b524..fdd645298 100644
--- a/doc/pub/week48/html/._week48-bs047.html
+++ b/doc/pub/week48/html/._week48-bs047.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,20 +258,40 @@ MathJax.Hub.Config({
 
 
 
-
    Transfer learning 
    
+
    Autoencoders: Overarching view 
    
 
 
    
-The goal of transfer learning is to transfer the model or knowledge
-obtained from a source task to the target task, in order to resolve
-the issues of insufficient training data in the target task. The
-rationality of doing so lies in that usually the source and target
-tasks have inter-correlations, and therefore either the features,
-samples, or models in the source task might provide useful information
-for us to better solve the target task. Transfer learning is a hot
-research topic in recent years, with many problems still waiting to be studied.
+Autoencoders are artificial neural networks capable of learning
+efficient representations of the input data (these representations are called codings)  without
+any supervision (i.e., the training set is unlabeled). These codings
+typically have a much lower dimensionality than the input data, making
+autoencoders useful for dimensionality reduction.
 
 
    
-Lecture on transfer learning.
+More importantly, autoencoders act as powerful feature detectors, and
+they can be used for unsupervised pretraining of deep neural networks.
+
+
    
+Lastly, they are capable of randomly generating new data that looks
+very similar to the training data; this is called a generative
+model. For example, you could train an autoencoder on pictures of
+faces, and it would then be able to generate new faces.  Surprisingly,
+autoencoders work by simply learning to copy their inputs to their
+outputs. This may sound like a trivial task, but we will see that
+constraining the network in various ways can make it rather
+difficult. For example, you can limit the size of the internal
+representation, or you can add noise to the inputs and train the
+network to recover the original inputs. These constraints prevent the
+autoencoder from trivially copying the inputs directly to the outputs,
+which forces it to learn efficient ways of representing the data. In
+short, the codings are byproducts of the autoencoder’s attempt to
+learn the identity function under some constraints.
+
+
    
+Video on autoencoders
+
+
    
+See also A. Geron's textbook, chapter 15.
 
 
    
 
    
@@ -282,7 +319,7 @@ research topic in recent years, with many problems still waiting to be studied.
   
  • 56
    • 
   
  • 57
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs048.html b/doc/pub/week48/html/._week48-bs048.html
index 19cb23977..8ab62d4a0 100644
--- a/doc/pub/week48/html/._week48-bs048.html
+++ b/doc/pub/week48/html/._week48-bs048.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,21 +258,24 @@ MathJax.Hub.Config({
 
 
 
-
    Adversarial learning 
    
+
    Bayesian Machine Learning 
    
 
 
    
-The conventional deep generative model has a potential problem: the
-model tends to generate extreme instances to maximize the
-probabilistic likelihood, which will hurt its performance. Adversarial
-learning utilizes the adversarial behaviors (e.g., generating
-adversarial instances or training an adversarial model) to enhance the
-robustness of the model and improve the quality of the generated
-data. In recent years, one of the most promising unsupervised learning
-technologies, generative adversarial networks (GAN), has already been
-successfully applied to image, speech, and text.
+This is an important topic if we aim at extracting a probability
+distribution. This gives us also a confidence interval and error
+estimates.
 
 
    
-Lecture on adversial learning.
+Bayesian machine learning allows us to encode our prior beliefs about
+what those models should look like, independent of what the data tells
+us. This is especially useful when we don’t have a ton of data to
+confidently learn our model.
+
+
    
+Video on Bayesian deep learning
+
+
    
+See also the slides here.
 
 
    
 
    
@@ -283,7 +303,7 @@ successfully applied to image, speech, and text.
   
  • 57
    • 
   
  • 58
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs049.html b/doc/pub/week48/html/._week48-bs049.html
index 99b6700cd..1a4d0bf3a 100644
--- a/doc/pub/week48/html/._week48-bs049.html
+++ b/doc/pub/week48/html/._week48-bs049.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,20 +258,38 @@ MathJax.Hub.Config({
 
 
 
-
    Dual learning 
    
+
    Reinforcement Learning 
    
 
 
    
-Dual learning is a new learning paradigm, the basic idea of which is
-to use the primal-dual structure between machine learning tasks to
-obtain effective feedback/regularization, and guide and strengthen the
-learning process, thus reducing the requirement of large-scale labeled
-data for deep learning. The idea of dual learning has been applied to
-many problems in machine learning, including machine translation,
-image style conversion, question answering and generation, image
-classification and generation, text classification and generation,
-image-to-text, and text-to-image.
+Reinforcement Learning (RL) is one of the most exciting fields of
+Machine Learning today, and also one of the oldest. It has been around
+since the 1950s, producing many interesting applications over the
+years.
 
 
    
+It studies
+how agents take actions based on trial and error, so as to maximize
+some notion of cumulative reward in a dynamic system or
+environment. Due to its generality, the problem has also been studied
+in many other disciplines, such as game theory, control theory,
+operations research, information theory, multi-agent systems, swarm
+intelligence, statistics, and genetic algorithms.
+
+
    
+In March 2016, AlphaGo, a computer program that plays the board game
+Go, beat Lee Sedol in a five-game match. This was the first time a
+computer Go program had beaten a 9-dan (highest rank) professional
+without handicaps. AlphaGo is based on deep convolutional neural
+networks and reinforcement learning. AlphaGo’s victory was a major
+milestone in artificial intelligence and it has also made
+reinforcement learning a hot research area in the field of machine
+learning.
+
+
    
+Lecture on Reinforcement Learning.
+
+
    
+See also A. Geron's textbook, chapter 16.
 
    
 
 
      
@@ -280,7 +315,7 @@ image-to-text, and text-to-image.
   
    • 58
      • 
   
    • 59
      • 
   
    • ...
      • 
-  
    • 61
      • 
+  
    • 64
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week48/html/._week48-bs050.html b/doc/pub/week48/html/._week48-bs050.html
index 32491e4fa..6f1195065 100644
--- a/doc/pub/week48/html/._week48-bs050.html
+++ b/doc/pub/week48/html/._week48-bs050.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,13 +258,20 @@ MathJax.Hub.Config({
 
 
 
-
    Distributed machine learning 
    
+
    Transfer learning 
    
 
 
    
-Distributed computation will speed up machine learning algorithms,
-significantly improve their efficiency, and thus enlarge their
-application. When distributed meets machine learning, more than just
-implementing the machine learning algorithms in parallel is required.
+The goal of transfer learning is to transfer the model or knowledge
+obtained from a source task to the target task, in order to resolve
+the issues of insufficient training data in the target task. The
+rationality of doing so lies in that usually the source and target
+tasks have inter-correlations, and therefore either the features,
+samples, or models in the source task might provide useful information
+for us to better solve the target task. Transfer learning is a hot
+research topic in recent years, with many problems still waiting to be studied.
+
+
    
+Lecture on transfer learning.
 
 
    
 
    
@@ -275,7 +299,7 @@ implementing the machine learning algorithms in parallel is required.
   
  • 59
    • 
   
  • 60
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs051.html b/doc/pub/week48/html/._week48-bs051.html
index 311a4db43..5a0e88140 100644
--- a/doc/pub/week48/html/._week48-bs051.html
+++ b/doc/pub/week48/html/._week48-bs051.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,16 +258,21 @@ MathJax.Hub.Config({
 
 
 
-
    Meta learning 
    
+
    Adversarial learning 
    
 
 
    
-Meta learning is an emerging research direction in machine
-learning. Roughly speaking, meta learning concerns learning how to
-learn, and focuses on the understanding and adaptation of the learning
-itself, instead of just completing a specific learning task. That is,
-a meta learner needs to be able to evaluate its own learning methods
-and adjust its own learning methods according to specific learning
-tasks.
+The conventional deep generative model has a potential problem: the
+model tends to generate extreme instances to maximize the
+probabilistic likelihood, which will hurt its performance. Adversarial
+learning utilizes the adversarial behaviors (e.g., generating
+adversarial instances or training an adversarial model) to enhance the
+robustness of the model and improve the quality of the generated
+data. In recent years, one of the most promising unsupervised learning
+technologies, generative adversarial networks (GAN), has already been
+successfully applied to image, speech, and text.
+
+
    
+Lecture on adversial learning.
 
 
    
 
    
@@ -277,6 +299,8 @@ tasks.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • ...
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs052.html b/doc/pub/week48/html/._week48-bs052.html
index 6bc60ad03..c10283e58 100644
--- a/doc/pub/week48/html/._week48-bs052.html
+++ b/doc/pub/week48/html/._week48-bs052.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,27 +258,18 @@ MathJax.Hub.Config({
 
 
 
-
    The Challenges Facing Machine Learning 
    
+
    Dual learning 
    
 
 
    
-While there has been much progress in machine learning, there are also challenges.
-
-
    
-For example, the mainstream machine learning technologies are
-black-box approaches, making us concerned about their potential
-risks. To tackle this challenge, we may want to make machine learning
-more explainable and controllable. As another example, the
-computational complexity of machine learning algorithms is usually
-very high and we may want to invent lightweight algorithms or
-implementations. Furthermore, in many domains such as physics,
-chemistry, biology, and social sciences, people usually seek elegantly
-simple equations (e.g., the Schrödinger equation) to uncover the
-underlying laws behind various phenomena. In the field of machine
-learning, can we reveal simple laws instead of designing more complex
-models for data fitting? Although there are many challenges, we are
-still very optimistic about the future of machine learning. As we look
-forward to the future, here are what we think the research hotspots in
-the next ten years will be.
+Dual learning is a new learning paradigm, the basic idea of which is
+to use the primal-dual structure between machine learning tasks to
+obtain effective feedback/regularization, and guide and strengthen the
+learning process, thus reducing the requirement of large-scale labeled
+data for deep learning. The idea of dual learning has been applied to
+many problems in machine learning, including machine translation,
+image style conversion, question answering and generation, image
+classification and generation, text classification and generation,
+image-to-text, and text-to-image.
 
 
    
 
    
@@ -287,6 +295,9 @@ the next ten years will be.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • ...
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs053.html b/doc/pub/week48/html/._week48-bs053.html
index 3b432524c..c67c70023 100644
--- a/doc/pub/week48/html/._week48-bs053.html
+++ b/doc/pub/week48/html/._week48-bs053.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,27 +258,13 @@ MathJax.Hub.Config({
 
 
 
-
    Explainable machine learning 
    
+
    Distributed machine learning 
    
 
 
    
-Machine learning, especially deep learning, evolves rapidly. The
-ability gap between machine and human on many complex cognitive tasks
-becomes narrower and narrower. However, we are still in the very early
-stage in terms of explaining why those effective models work and how
-they work.
-
-
    
-What is missing: the gap between correlation and causation. Standard Machine Learning is based on what e have called a frequentist approach.
-
-
    
-Most
-machine learning techniques, especially the statistical ones, depend
-highly on correlations in data sets to make predictions and analyses. In
-contrast, rational humans tend to reply on clear and trustworthy
-causality relations obtained via logical reasoning on real and clear
-facts. It is one of the core goals of explainable machine learning to
-transition from solving problems by data correlation to solving
-problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
+Distributed computation will speed up machine learning algorithms,
+significantly improve their efficiency, and thus enlarge their
+application. When distributed meets machine learning, more than just
+implementing the machine learning algorithms in parallel is required.
 
 
    
 
    
@@ -286,6 +289,10 @@ problems by logical reasoning. Bayesian Machine Learning is one of the exciting
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • ...
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs054.html b/doc/pub/week48/html/._week48-bs054.html
index 97144a3f4..df1381181 100644
--- a/doc/pub/week48/html/._week48-bs054.html
+++ b/doc/pub/week48/html/._week48-bs054.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,33 +258,16 @@ MathJax.Hub.Config({
 
 
 
-
    Quantum machine learning 
    
+
    Meta learning 
    
 
 
    
-Quantum machine learning is an emerging interdisciplinary research
-area at the intersection of quantum computing and machine learning.
-
-
    
-Quantum computers use effects such as quantum coherence and quantum
-entanglement to process information, which is fundamentally different
-from classical computers. Quantum algorithms have surpassed the best
-classical algorithms in several problems (e.g., searching for an
-unsorted database, inverting a sparse matrix), which we call quantum
-acceleration.
-
-
    
-When quantum computing meets machine learning, it can be a mutually
-beneficial and reinforcing process, as it allows us to take advantage
-of quantum computing to improve the performance of classical machine
-learning algorithms. In addition, we can also use the machine learning
-algorithms (on classic computers) to analyze and improve quantum
-computing systems.
-
-
    
-Lecture on Quantum ML.
-
-
    
-Read interview with Maria Schuld on her work on Quantum Machine Learning. See also her recent textbook.
+Meta learning is an emerging research direction in machine
+learning. Roughly speaking, meta learning concerns learning how to
+learn, and focuses on the understanding and adaptation of the learning
+itself, instead of just completing a specific learning task. That is,
+a meta learner needs to be able to evaluate its own learning methods
+and adjust its own learning methods according to specific learning
+tasks.
 
 
    
 
    
@@ -291,6 +291,9 @@ computing systems.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs055.html b/doc/pub/week48/html/._week48-bs055.html
index d547f7639..7dbe7c84d 100644
--- a/doc/pub/week48/html/._week48-bs055.html
+++ b/doc/pub/week48/html/._week48-bs055.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,21 +258,27 @@ MathJax.Hub.Config({
 
 
 
-
    Quantum machine learning algorithms based on linear algebra 
    
+
    The Challenges Facing Machine Learning 
    
 
 
    
-Many quantum machine learning algorithms are based on variants of
-quantum algorithms for solving linear equations, which can efficiently
-solve N-variable linear equations with complexity of O(log2 N) under
-certain conditions. The quantum matrix inversion algorithm can
-accelerate many machine learning methods, such as least square linear
-regression, least square version of support vector machine, Gaussian
-process, and more. The training of these algorithms can be simplified
-to solve linear equations. The key bottleneck of this type of quantum
-machine learning algorithms is data input—that is, how to initialize
-the quantum system with the entire data set. Although efficient
-data-input algorithms exist for certain situations, how to efficiently
-input data into a quantum system is as yet unknown for most cases.
+While there has been much progress in machine learning, there are also challenges.
+
+
    
+For example, the mainstream machine learning technologies are
+black-box approaches, making us concerned about their potential
+risks. To tackle this challenge, we may want to make machine learning
+more explainable and controllable. As another example, the
+computational complexity of machine learning algorithms is usually
+very high and we may want to invent lightweight algorithms or
+implementations. Furthermore, in many domains such as physics,
+chemistry, biology, and social sciences, people usually seek elegantly
+simple equations (e.g., the Schrödinger equation) to uncover the
+underlying laws behind various phenomena. In the field of machine
+learning, can we reveal simple laws instead of designing more complex
+models for data fitting? Although there are many challenges, we are
+still very optimistic about the future of machine learning. As we look
+forward to the future, here are what we think the research hotspots in
+the next ten years will be.
 
 
    
 
    
@@ -278,6 +301,9 @@ input data into a quantum system is as yet unknown for most cases.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs056.html b/doc/pub/week48/html/._week48-bs056.html
index 7daf3d2ef..93dc8e732 100644
--- a/doc/pub/week48/html/._week48-bs056.html
+++ b/doc/pub/week48/html/._week48-bs056.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,16 +258,27 @@ MathJax.Hub.Config({
 
 
 
-
    Quantum reinforcement learning 
    
+
    Explainable machine learning 
    
 
 
    
-In quantum reinforcement learning, a quantum agent interacts with the
-classical environment to obtain rewards from the environment, so as to
-adjust and improve its behavioral strategies. In some cases, it
-achieves quantum acceleration by the quantum processing capabilities
-of the agent or the possibility of exploring the environment through
-quantum superposition. Such algorithms have been proposed in
-superconducting circuits and systems of trapped ions.
+Machine learning, especially deep learning, evolves rapidly. The
+ability gap between machine and human on many complex cognitive tasks
+becomes narrower and narrower. However, we are still in the very early
+stage in terms of explaining why those effective models work and how
+they work.
+
+
    
+What is missing: the gap between correlation and causation. Standard Machine Learning is based on what e have called a frequentist approach.
+
+
    
+Most
+machine learning techniques, especially the statistical ones, depend
+highly on correlations in data sets to make predictions and analyses. In
+contrast, rational humans tend to reply on clear and trustworthy
+causality relations obtained via logical reasoning on real and clear
+facts. It is one of the core goals of explainable machine learning to
+transition from solving problems by data correlation to solving
+problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
 
 
    
 
    
@@ -272,6 +300,9 @@ superconducting circuits and systems of trapped ions.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs057.html b/doc/pub/week48/html/._week48-bs057.html
index f10c380b3..718637db8 100644
--- a/doc/pub/week48/html/._week48-bs057.html
+++ b/doc/pub/week48/html/._week48-bs057.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,21 +258,33 @@ MathJax.Hub.Config({
 
 
 
-
    Quantum deep learning 
    
+
    Quantum machine learning 
    
 
 
    
-Dedicated quantum information processors, such as quantum annealers
-and programmable photonic circuits, are well suited for building deep
-quantum networks. The simplest deep quantum network is the Boltzmann
-machine. The classical Boltzmann machine consists of bits with tunable
-interactions and is trained by adjusting the interaction of these bits
-so that the distribution of its expression conforms to the statistics
-of the data. To quantize the Boltzmann machine, the neural network can
-simply be represented as a set of interacting quantum spins that
-correspond to an adjustable Ising model. Then, by initializing the
-input neurons in the Boltzmann machine to a fixed state and allowing
-the system to heat up, we can read out the output qubits to get the
-result.
+Quantum machine learning is an emerging interdisciplinary research
+area at the intersection of quantum computing and machine learning.
+
+
    
+Quantum computers use effects such as quantum coherence and quantum
+entanglement to process information, which is fundamentally different
+from classical computers. Quantum algorithms have surpassed the best
+classical algorithms in several problems (e.g., searching for an
+unsorted database, inverting a sparse matrix), which we call quantum
+acceleration.
+
+
    
+When quantum computing meets machine learning, it can be a mutually
+beneficial and reinforcing process, as it allows us to take advantage
+of quantum computing to improve the performance of classical machine
+learning algorithms. In addition, we can also use the machine learning
+algorithms (on classic computers) to analyze and improve quantum
+computing systems.
+
+
    
+Lecture on Quantum ML.
+
+
    
+Read interview with Maria Schuld on her work on Quantum Machine Learning. See also her recent textbook.
 
 
    
 
    
@@ -276,6 +305,9 @@ result.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs058.html b/doc/pub/week48/html/._week48-bs058.html
index 395e669b7..120ca9bb1 100644
--- a/doc/pub/week48/html/._week48-bs058.html
+++ b/doc/pub/week48/html/._week48-bs058.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,20 +258,21 @@ MathJax.Hub.Config({
 
 
 
-
    Social machine learning 
    
+
    Quantum machine learning algorithms based on linear algebra 
    
 
 
    
-Machine learning aims to imitate how humans
-learn. While we have developed successful machine learning algorithms,
-until now we have ignored one important fact: humans are social. Each
-of us is one part of the total society and it is difficult for us to
-live, learn, and improve ourselves, alone and isolated. Therefore, we
-should design machines with social properties. Can we let machines
-evolve by imitating human society so as to achieve more effective,
-intelligent, interpretable “social machine learning”?
-
-
    
-And much more.
+Many quantum machine learning algorithms are based on variants of
+quantum algorithms for solving linear equations, which can efficiently
+solve N-variable linear equations with complexity of O(log2 N) under
+certain conditions. The quantum matrix inversion algorithm can
+accelerate many machine learning methods, such as least square linear
+regression, least square version of support vector machine, Gaussian
+process, and more. The training of these algorithms can be simplified
+to solve linear equations. The key bottleneck of this type of quantum
+machine learning algorithms is data input—that is, how to initialize
+the quantum system with the entire data set. Although efficient
+data-input algorithms exist for certain situations, how to efficiently
+input data into a quantum system is as yet unknown for most cases.
 
 
    
 
    
@@ -274,6 +292,9 @@ And much more.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs059.html b/doc/pub/week48/html/._week48-bs059.html
index 6fe7b35f4..10bf653ab 100644
--- a/doc/pub/week48/html/._week48-bs059.html
+++ b/doc/pub/week48/html/._week48-bs059.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,14 +258,16 @@ MathJax.Hub.Config({
 
 
 
-
    The last words? 
    
+
    Quantum reinforcement learning 
    
 
 
    
-Early computer scientist Alan Kay said, The best way to predict the
-future is to create it. Therefore, all machine learning
-practitioners, whether scholars or engineers, professors or students,
-need to work together to advance these important research
-topics. Together, we will not just predict the future, but create it.
+In quantum reinforcement learning, a quantum agent interacts with the
+classical environment to obtain rewards from the environment, so as to
+adjust and improve its behavioral strategies. In some cases, it
+achieves quantum acceleration by the quantum processing capabilities
+of the agent or the possibility of exploring the environment through
+quantum superposition. Such algorithms have been proposed in
+superconducting circuits and systems of trapped ions.
 
 
    
 
    
@@ -267,6 +286,9 @@ topics. Together, we will not just predict the future, but create it.
   
  • 59
    • 
   
  • 60
    • 
   
  • 61
    • 
+  
  • 62
    • 
+  
  • 63
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/._week48-bs060.html b/doc/pub/week48/html/._week48-bs060.html
index b1806d3ab..e2a72ab3e 100644
--- a/doc/pub/week48/html/._week48-bs060.html
+++ b/doc/pub/week48/html/._week48-bs060.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -241,13 +258,23 @@ MathJax.Hub.Config({
 
 
 
-
    Best wishes to you all and thanks so much for your heroic efforts this semester 
    
+
    Quantum deep learning 
    
 
 
    
-



    
+Dedicated quantum information processors, such as quantum annealers
+and programmable photonic circuits, are well suited for building deep
+quantum networks. The simplest deep quantum network is the Boltzmann
+machine. The classical Boltzmann machine consists of bits with tunable
+interactions and is trained by adjusting the interaction of these bits
+so that the distribution of its expression conforms to the statistics
+of the data. To quantize the Boltzmann machine, the neural network can
+simply be represented as a set of interacting quantum spins that
+correspond to an adjustable Ising model. Then, by initializing the
+input neurons in the Boltzmann machine to a fixed state and allowing
+the system to heat up, we can read out the output qubits to get the
+result.
 
 
    
-
 
    
 
 
      
@@ -263,6 +290,10 @@ MathJax.Hub.Config({
   
    • 59
      • 
   
    • 60
      • 
   
    • 61
      • 
+  
    • 62
      • 
+  
    • 63
      • 
+  
    • 64
      • 
+  
    • »
      • 
 
    
 
 
diff --git a/doc/pub/week48/html/week48-bs.html b/doc/pub/week48/html/week48-bs.html
index 341424093..dc68b9446 100644
--- a/doc/pub/week48/html/week48-bs.html
+++ b/doc/pub/week48/html/week48-bs.html
@@ -48,87 +48,101 @@ Automatically generated HTML file from DocOnce source
               ('Kernels and non-linearity', 2, None, '___sec4'),
               ('The equations', 2, None, '___sec5'),
               ('The problem to solve', 2, None, '___sec6'),
-              ("Different kernels and Mercer's theorem", 2, None, '___sec7'),
-              ('The moons example', 2, None, '___sec8'),
-              ('Mathematical optimization of convex functions',
+              ('Tailoring the equations to the usage of CVXOPT',
+               2,
+               None,
+               '___sec7'),
+              ("Different kernels and Mercer's theorem", 2, None, '___sec8'),
+              ('The moons example ("Adapted from Geron, chapter '
+               '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")',
                2,
                None,
                '___sec9'),
-              ('How do we solve these problems?', 2, None, '___sec10'),
-              ('A simple example', 2, None, '___sec11'),
-              ('Back to the more realistic cases', 2, None, '___sec12'),
-              ('Summary of course', 2, None, '___sec13'),
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec10'),
+              ('How do we solve these problems?', 2, None, '___sec11'),
+              ('A simple example', 2, None, '___sec12'),
+              ('Back to the more realistic cases', 2, None, '___sec13'),
+              ('Setting up the matrices and the problem', 2, None, '___sec14'),
+              ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq '
+               '\\boldsymbol{h}$',
+               2,
+               None,
+               '___sec15'),
+              ('Summary of course', 2, None, '___sec16'),
               ('What? Me worry? No final exam in this course!',
                2,
                None,
-               '___sec14'),
-              ('Topics we have covered this year', 2, None, '___sec15'),
+               '___sec17'),
+              ('Topics we have covered this year', 2, None, '___sec18'),
               ('Statistical analysis and optimization of data',
                2,
                None,
-               '___sec16'),
-              ('Machine learning', 2, None, '___sec17'),
+               '___sec19'),
+              ('Machine learning', 2, None, '___sec20'),
               ('Learning outcomes and overarching aims of this course',
                2,
                None,
-               '___sec18'),
-              ('Perspective on Machine Learning', 2, None, '___sec19'),
-              ('Machine Learning Research', 2, None, '___sec20'),
-              ('Starting your Machine Learning Project', 2, None, '___sec21'),
-              ('Choose a Model and Algorithm', 2, None, '___sec22'),
-              ('Preparing Your Data', 2, None, '___sec23'),
+               '___sec21'),
+              ('Perspective on Machine Learning', 2, None, '___sec22'),
+              ('Machine Learning Research', 2, None, '___sec23'),
+              ('Starting your Machine Learning Project', 2, None, '___sec24'),
+              ('Choose a Model and Algorithm', 2, None, '___sec25'),
+              ('Preparing Your Data', 2, None, '___sec26'),
               ('Which Activation and Weights to Choose in Neural Networks',
                2,
                None,
-               '___sec24'),
-              ('Optimization Methods and Hyperparameters', 2, None, '___sec25'),
-              ('Resampling', 2, None, '___sec26'),
+               '___sec27'),
+              ('Optimization Methods and Hyperparameters', 2, None, '___sec28'),
+              ('Resampling', 2, None, '___sec29'),
               ('Other courses on Data science and Machine Learning  at UiO',
                2,
                None,
-               '___sec27'),
-              ('Additional courses of interest', 2, None, '___sec28'),
-              ("What's the future like?", 2, None, '___sec29'),
-              ('Types of Machine Learning, a repetition', 2, None, '___sec30'),
-              ('Why Boltzmann machines?', 2, None, '___sec31'),
-              ('Boltzmann Machines', 2, None, '___sec32'),
+               '___sec30'),
+              ('Additional courses of interest', 2, None, '___sec31'),
+              ("What's the future like?", 2, None, '___sec32'),
+              ('Types of Machine Learning, a repetition', 2, None, '___sec33'),
+              ('Why Boltzmann machines?', 2, None, '___sec34'),
+              ('Boltzmann Machines', 2, None, '___sec35'),
               ('Some similarities and differences from DNNs',
                2,
                None,
-               '___sec33'),
-              ('Boltzmann machines (BM)', 2, None, '___sec34'),
-              ('A standard BM setup', 2, None, '___sec35'),
-              ('The structure of the RBM network', 2, None, '___sec36'),
-              ('The network', 2, None, '___sec37'),
-              ('Goals', 2, None, '___sec38'),
-              ('Joint distribution', 2, None, '___sec39'),
-              ('Network Elements, the energy function', 2, None, '___sec40'),
-              ('Defining different types of RBMs', 2, None, '___sec41'),
-              ('More about RBMs', 2, None, '___sec42'),
-              ('Autoencoders: Overarching view', 2, None, '___sec43'),
-              ('Bayesian Machine Learning', 2, None, '___sec44'),
-              ('Reinforcement Learning', 2, None, '___sec45'),
-              ('Transfer learning', 2, None, '___sec46'),
-              ('Adversarial learning', 2, None, '___sec47'),
-              ('Dual learning', 2, None, '___sec48'),
-              ('Distributed machine learning', 2, None, '___sec49'),
-              ('Meta learning', 2, None, '___sec50'),
-              ('The Challenges Facing Machine Learning', 2, None, '___sec51'),
-              ('Explainable machine learning', 2, None, '___sec52'),
-              ('Quantum machine learning', 2, None, '___sec53'),
+               '___sec36'),
+              ('Boltzmann machines (BM)', 2, None, '___sec37'),
+              ('A standard BM setup', 2, None, '___sec38'),
+              ('The structure of the RBM network', 2, None, '___sec39'),
+              ('The network', 2, None, '___sec40'),
+              ('Goals', 2, None, '___sec41'),
+              ('Joint distribution', 2, None, '___sec42'),
+              ('Network Elements, the energy function', 2, None, '___sec43'),
+              ('Defining different types of RBMs', 2, None, '___sec44'),
+              ('More about RBMs', 2, None, '___sec45'),
+              ('Autoencoders: Overarching view', 2, None, '___sec46'),
+              ('Bayesian Machine Learning', 2, None, '___sec47'),
+              ('Reinforcement Learning', 2, None, '___sec48'),
+              ('Transfer learning', 2, None, '___sec49'),
+              ('Adversarial learning', 2, None, '___sec50'),
+              ('Dual learning', 2, None, '___sec51'),
+              ('Distributed machine learning', 2, None, '___sec52'),
+              ('Meta learning', 2, None, '___sec53'),
+              ('The Challenges Facing Machine Learning', 2, None, '___sec54'),
+              ('Explainable machine learning', 2, None, '___sec55'),
+              ('Quantum machine learning', 2, None, '___sec56'),
               ('Quantum machine learning algorithms based on linear algebra',
                2,
                None,
-               '___sec54'),
-              ('Quantum reinforcement learning', 2, None, '___sec55'),
-              ('Quantum deep learning', 2, None, '___sec56'),
-              ('Social machine learning', 2, None, '___sec57'),
-              ('The last words?', 2, None, '___sec58'),
+               '___sec57'),
+              ('Quantum reinforcement learning', 2, None, '___sec58'),
+              ('Quantum deep learning', 2, None, '___sec59'),
+              ('Social machine learning', 2, None, '___sec60'),
+              ('The last words?', 2, None, '___sec61'),
               ('Best wishes to you all and thanks so much for your heroic '
                'efforts this semester',
                2,
                None,
-               '___sec59')]}
+               '___sec62')]}
 end of tocinfo -->
 
 
@@ -173,59 +187,62 @@ MathJax.Hub.Config({
       
  • Kernels and non-linearity
    • 
       
  • The equations
    • 
       
  • The problem to solve
    • 
-      
  • Different kernels and Mercer's theorem
    • 
-      
  • The moons example
    • 
-      
  • Mathematical optimization of convex functions
    • 
-      
  • How do we solve these problems?
    • 
-      
  • A simple example
    • 
-      
  • Back to the more realistic cases
    • 
-      
  • Summary of course
    • 
-      
  • What? Me worry? No final exam in this course!
    • 
-      
  • Topics we have covered this year
    • 
-      
  • Statistical analysis and optimization of data
    • 
-      
  • Machine learning
    • 
-      
  • Learning outcomes and overarching aims of this course
    • 
-      
  • Perspective on Machine Learning
    • 
-      
  • Machine Learning Research
    • 
-      
  • Starting your Machine Learning Project
    • 
-      
  • Choose a Model and Algorithm
    • 
-      
  • Preparing Your Data
    • 
-      
  • Which Activation and Weights to Choose in Neural Networks
    • 
-      
  • Optimization Methods and Hyperparameters
    • 
-      
  • Resampling
    • 
-      
  • Other courses on Data science and Machine Learning  at UiO
    • 
-      
  • Additional courses of interest
    • 
-      
  • What's the future like?
    • 
-      
  • Types of Machine Learning, a repetition
    • 
-      
  • Why Boltzmann machines?
    • 
-      
  • Boltzmann Machines
    • 
-      
  • Some similarities and differences from DNNs
    • 
-      
  • Boltzmann machines (BM)
    • 
-      
  • A standard BM setup
    • 
-      
  • The structure of the RBM network
    • 
-      
  • The network
    • 
-      
  • Goals
    • 
-      
  • Joint distribution
    • 
-      
  • Network Elements, the energy function
    • 
-      
  • Defining different types of RBMs
    • 
-      
  • More about RBMs
    • 
-      
  • Autoencoders: Overarching view
    • 
-      
  • Bayesian Machine Learning
    • 
-      
  • Reinforcement Learning
    • 
-      
  • Transfer learning
    • 
-      
  • Adversarial learning
    • 
-      
  • Dual learning
    • 
-      
  • Distributed machine learning
    • 
-      
  • Meta learning
    • 
-      
  • The Challenges Facing Machine Learning
    • 
-      
  • Explainable machine learning
    • 
-      
  • Quantum machine learning
    • 
-      
  • Quantum machine learning algorithms based on linear algebra
    • 
-      
  • Quantum reinforcement learning
    • 
-      
  • Quantum deep learning
    • 
-      
  • Social machine learning
    • 
-      
  • The last words?
    • 
-      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
+      
  • Tailoring the equations to the usage of CVXOPT
    • 
+      
  • Different kernels and Mercer's theorem
    • 
+      
  • The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")
    • 
+      
  • Mathematical optimization of convex functions
    • 
+      
  • How do we solve these problems?
    • 
+      
  • A simple example
    • 
+      
  • Back to the more realistic cases
    • 
+      
  • Setting up the matrices and the problem
    • 
+      
  • Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)
    • 
+      
  • Summary of course
    • 
+      
  • What? Me worry? No final exam in this course!
    • 
+      
  • Topics we have covered this year
    • 
+      
  • Statistical analysis and optimization of data
    • 
+      
  • Machine learning
    • 
+      
  • Learning outcomes and overarching aims of this course
    • 
+      
  • Perspective on Machine Learning
    • 
+      
  • Machine Learning Research
    • 
+      
  • Starting your Machine Learning Project
    • 
+      
  • Choose a Model and Algorithm
    • 
+      
  • Preparing Your Data
    • 
+      
  • Which Activation and Weights to Choose in Neural Networks
    • 
+      
  • Optimization Methods and Hyperparameters
    • 
+      
  • Resampling
    • 
+      
  • Other courses on Data science and Machine Learning  at UiO
    • 
+      
  • Additional courses of interest
    • 
+      
  • What's the future like?
    • 
+      
  • Types of Machine Learning, a repetition
    • 
+      
  • Why Boltzmann machines?
    • 
+      
  • Boltzmann Machines
    • 
+      
  • Some similarities and differences from DNNs
    • 
+      
  • Boltzmann machines (BM)
    • 
+      
  • A standard BM setup
    • 
+      
  • The structure of the RBM network
    • 
+      
  • The network
    • 
+      
  • Goals
    • 
+      
  • Joint distribution
    • 
+      
  • Network Elements, the energy function
    • 
+      
  • Defining different types of RBMs
    • 
+      
  • More about RBMs
    • 
+      
  • Autoencoders: Overarching view
    • 
+      
  • Bayesian Machine Learning
    • 
+      
  • Reinforcement Learning
    • 
+      
  • Transfer learning
    • 
+      
  • Adversarial learning
    • 
+      
  • Dual learning
    • 
+      
  • Distributed machine learning
    • 
+      
  • Meta learning
    • 
+      
  • The Challenges Facing Machine Learning
    • 
+      
  • Explainable machine learning
    • 
+      
  • Quantum machine learning
    • 
+      
  • Quantum machine learning algorithms based on linear algebra
    • 
+      
  • Quantum reinforcement learning
    • 
+      
  • Quantum deep learning
    • 
+      
  • Social machine learning
    • 
+      
  • The last words?
    • 
+      
  • Best wishes to you all and thanks so much for your heroic efforts this semester
    • 
 
         
       
@@ -260,7 +277,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Nov 25, 2020
     
+
    Nov 26, 2020
     
 
    
 
    
 
@@ -284,7 +301,7 @@ MathJax.Hub.Config({
   
  • 9
    • 
   
  • 10
    • 
   
  • ...
    • 
-  
  • 61
    • 
+  
  • 64
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week48/html/week48-reveal.html b/doc/pub/week48/html/week48-reveal.html
index dc26acaf6..ebcfa4cd8 100644
--- a/doc/pub/week48/html/week48-reveal.html
+++ b/doc/pub/week48/html/week48-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
     
    
-
    Nov 25, 2020
     
+
    Nov 26, 2020
     
 
    
 
    
 
@@ -229,13 +229,13 @@ wavelets, splines etc.
 
 
    
 If our feature space is not easy to separate, as shown in the figure
-here, we can achieve a better separation by introducing more complex
-basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to 
+here generated by the code below (see also Figures 12.2 and 12.3 of Hastie et al.), we can achieve a better separation by introducing more complex
+basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to 
 obtain a separation between the classes which is almost linear.
 
 
    
 The change of basis, from \( x\rightarrow z=\phi(x) \) leads to the same type of equations to be solved, except that
-we need to introduce for example a polynomial transformation to a two-dimensional training set.
+we need to introduce, for example, a polynomial transformation to a two-dimensional training set.
 
 
    
 
@@ -297,7 +297,7 @@ plt.show()
 Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
 
     
    
 $$
-z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 $$
 
     
    
 
@@ -312,7 +312,7 @@ $$
 subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \), and for the support vectors
 
     
    
 $$
-y_i(\boldsymbol{w}^T\boldsymbol{z}_i+b)= 1 \hspace{0.1cm}\forall i,
+y_i(\boldsymbol{z}_i^T\boldsymbol{w}+b)= 1 \hspace{0.1cm}\forall i,
 $$
 
     
    
 
@@ -327,27 +327,32 @@ $$
 For the above example, the kernel reads
 
     
    
 $$
-K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2.
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} 1\\ \sqrt{2}x_j \\ \sqrt{2}y_j \\ x_j^2\\ y_i^2\\ \sqrt{2}x_jy_j \end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j.
 $$
 
     
    
 
 
    
-We note that this is nothing but the dot product of the two original
-vectors \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). Instead of thus computing the
-product in the Lagrangian of \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we simply compute
-the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
+We note that this dot product can be rewritten as
+
     
    
+$$
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d,
+$$
+
     
    
 
-
    
+where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \).
+To compute the last equation is however inefficient from a computational stand.
+Instead of computing the last equation for the kernel, we simply compute
+the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
 This leads to the so-called
-kernel trick and the result leads to the same as if we went through
-the trouble of performing the transformation
-\( \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j) \) during the SVM calculations.
+kernel trick.
 
 
 
 
    
 
    The problem to solve 
    
-Using our definition of the kernel We can rewrite again the Lagrangian
+
+
    
+Using our definition of the kernel, we can rewrite again the Lagrangian
 
     
    
 $$
 {\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{z}_j,
@@ -369,6 +374,11 @@ $$
 subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and 
 \( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). 
 If we add the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
+
    
+
+
+
    
+
    Tailoring the equations to the usage of CVXOPT 
    
 
 
    
 We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type
@@ -388,7 +398,7 @@ Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
 
 
 
    
-
    Different kernels and Mercer's theorem 
    
+
    Different kernels and Mercer's theorem 
    
 
 
    
 There are several popular kernels being used. These are
@@ -429,7 +439,7 @@ in practice.
 
 
 
    
-
    The moons example 
    
+
    The moons example (Adapted from Geron, chapter 5) 
    
 
    
 
 
@@ -626,7 +636,7 @@ plt.show()
 
 
 
    
-
    Mathematical optimization of convex functions 
    
+
    Mathematical optimization of convex functions 
    
 
 
    
 A mathematical (quadratic) optimization problem, or just optimization problem, has the form
@@ -653,7 +663,7 @@ Convex optimization problems play a central role in applied mathematics and we r
 
 
 
    
-
    How do we solve these problems? 
    
+
    How do we solve these problems? 
    
 
 
    
 If we use Python as programming language and wish to venture beyond
@@ -674,12 +684,12 @@ The functions we need are contained in the quadratic programming package CVXO
 import cvxopt

    -This will make our life much easier. You don't need t write your own optimizer. +This will make our life much easier. You don't need to write your own optimizer.

    -

    A simple example

    +

    A simple example

    We remind ourselves about the general problem we want to solve @@ -760,7 +770,7 @@ sol[’primal obj

    -

    Back to the more realistic cases

    +

    Back to the more realistic cases

    We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the slack parameter \( C \) we have @@ -782,18 +792,91 @@ With the slack constants this leads to the additional constraint \( 0\leq \lamb

    -

    Summary of course

    +

    Setting up the matrices and the problem

    + +

    +We have the general problem +

     
    +$$ +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. +\end{align*} +$$ +

     
    + + +

      +

    1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
      2. +

    2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
      3. +

    3. The \( \boldsymbol{q} \) is zero.
      4. +

    4. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
      5. +

    5. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into
      6. +
    +

    + +\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).

    -

    What? Me worry? No final exam in this course!

    +

    Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)

    + +

    +We have two constraints, \( 0\le \lambda_i \) and \( \lambda_i \le C \). To do this we multiply the ones with the contraint +\( \ge \) with \( -1 \) in order to get \( \le \). It means that the problem \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) +can be written as +

     
    +$$ +\begin{bmatrix} -1& 0 & 0 & \dots & 0 \\ +0& -1 & 0 & \dots & 0 \\ +0& 0 & -1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & -1 \\ + -& 0 & 0 & \dots & 0 \\ +0& 1 & 0 & \dots & 0 \\ +0& 0 & 1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & 1 \\ +\end{bmatrix}\boldsymbol{\lambda} +\begin{bmatrix} \lambda_1 \\ +\lambda_2 \\ +\lambda_3 \\ +\dots \\ +\lambda_n \\ +\end{bmatrix}\boldsymbol{\lambda}= +\begin{bmatrix} 0 \\ +0 \\ +0 \\ +\dots \\ +0 \\ +C \\ +C \\ +C \\ +\dots \\ +C \\ +\end{bmatrix}\boldsymbol{\lambda} +$$ +

     
    + +

    +And then we are ready to go. +

    + + +
    +

    Summary of course

    +
    + + +
    +

    What? Me worry? No final exam in this course!





    -

    Topics we have covered this year

    +

    Topics we have covered this year

    The course has two central parts @@ -806,7 +889,7 @@ The course has two central parts

    -

    Statistical analysis and optimization of data

    +

    Statistical analysis and optimization of data

    The following topics be covered @@ -824,7 +907,7 @@ The following topics be covered

    -

    Machine learning

    +

    Machine learning

    The following topics will be covered @@ -866,7 +949,7 @@ The following topics will be covered

    -

    Learning outcomes and overarching aims of this course

    +

    Learning outcomes and overarching aims of this course

    The course introduces a variety of central algorithms and methods @@ -893,7 +976,7 @@ ethical conduct is emphasized throughout the course.

    -

    Perspective on Machine Learning

    +

    Perspective on Machine Learning

    1. Rapidly emerging application area
      2. @@ -911,7 +994,7 @@ Neural Networks, etc.
      -

      Machine Learning Research

      +

      Machine Learning Research

      Where to find recent results: @@ -927,7 +1010,7 @@ Where to find recent results:

      -

      Starting your Machine Learning Project

      +

      Starting your Machine Learning Project

      1. Identify problem type: classification, generation, regression
        2. @@ -940,7 +1023,7 @@ Where to find recent results:
        -

        Choose a Model and Algorithm

        +

        Choose a Model and Algorithm

        1. Supervised?
          2. @@ -951,7 +1034,7 @@ Where to find recent results:
          -

          Preparing Your Data

          +

          Preparing Your Data

          1. Shuffle your data
            2. @@ -981,7 +1064,7 @@ Where to find recent results:
            -

            Which Activation and Weights to Choose in Neural Networks

            +

            Which Activation and Weights to Choose in Neural Networks

            1. RELU? ELU?
              2. @@ -1004,7 +1087,7 @@ Where to find recent results:
              -

              Optimization Methods and Hyperparameters

              +

              Optimization Methods and Hyperparameters

              1. Stochastic gradient descent @@ -1029,7 +1112,7 @@ Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifie
                -

                Resampling

                +

                Resampling

                When do we resample? @@ -1043,7 +1126,7 @@ When do we resample?

                -

                Other courses on Data science and Machine Learning at UiO

                +

                Other courses on Data science and Machine Learning at UiO

                The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/ gives an excellent overview of courses on Machine learning at UiO. @@ -1062,7 +1145,7 @@ The link here Additional courses of interest +

                Additional courses of interest

                1. STK4051 Computational Statistics
                  2. @@ -1072,7 +1155,7 @@ The link here What's the future like? +

                  What's the future like?

                  Based on multi-layer nonlinear neural networks, deep learning can @@ -1096,7 +1179,7 @@ networks have been proposed, such as

                  -

                  Types of Machine Learning, a repetition

                  +

                  Types of Machine Learning, a repetition

                  @@ -1129,7 +1212,7 @@ Some of the most common tasks are:
                  -

                  Why Boltzmann machines?

                  +

                  Why Boltzmann machines?

                  What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. @@ -1144,7 +1227,7 @@ Furthermore, they have been used to solve complicated Boltzmann Machines +

                  Boltzmann Machines

                  Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? @@ -1164,7 +1247,7 @@ Why use a generative model rather than the more well known discriminative deep n

                  -

                  Some similarities and differences from DNNs

                  +

                  Some similarities and differences from DNNs

                  1. Both use gradient-descent based learning procedures for minimizing cost functions
                    2. @@ -1178,7 +1261,7 @@ History: The RBM was developed by amongst others                     Boltzmann machines (BM) +

                    Boltzmann machines (BM)

                    @@ -1209,7 +1292,7 @@ the learned distribution.
                    -

                    A standard BM setup

                    +

                    A standard BM setup

                    @@ -1239,7 +1322,7 @@ Here we take away all lateral connections between nodes in the visible layer as
                    -

                    The structure of the RBM network

                    +

                    The structure of the RBM network





                    @@ -1247,7 +1330,7 @@ Here we take away all lateral connections between nodes in the visible layer as
                    -

                    The network

                    +

                    The network

                    The network layers: @@ -1260,7 +1343,7 @@ Here we take away all lateral connections between nodes in the visible layer as

                    -

                    Goals

                    +

                    Goals

                    The goal of the hidden layer is to increase the model's expressive @@ -1282,7 +1365,7 @@ over (integrated out).

                    -

                    Joint distribution

                    +

                    Joint distribution

                    The restricted Boltzmann machine is described by a Bolztmann distribution @@ -1310,7 +1393,7 @@ It is common to ignore \( T_0 \) by setting it to one.

                    -

                    Network Elements, the energy function

                    +

                    Network Elements, the energy function

                    The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a @@ -1340,7 +1423,7 @@ The connection between the nodes in the two layers is given by the weights \( w_

                    -

                    Defining different types of RBMs

                    +

                    Defining different types of RBMs

                    There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function \( E(\mathbf{x},\mathbf{h}) \).

                    @@ -1377,7 +1460,7 @@ $$

                    -

                    More about RBMs

                    +

                    More about RBMs

                    1. Useful when we model continuous data (i.e., we wish \( \mathbf{x} \) to be continuous)
                      2. @@ -1397,7 +1480,7 @@ Other types of units include:
                      -

                      Autoencoders: Overarching view

                      +

                      Autoencoders: Overarching view

                      Autoencoders are artificial neural networks capable of learning @@ -1435,7 +1518,7 @@ See also A. Geron's textbook, chapter 15.

                      -

                      Bayesian Machine Learning

                      +

                      Bayesian Machine Learning

                      This is an important topic if we aim at extracting a probability @@ -1457,7 +1540,7 @@ See also the Reinforcement Learning +

                      Reinforcement Learning

                      Reinforcement Learning (RL) is one of the most exciting fields of @@ -1493,7 +1576,7 @@ See also A. Geron's textbook, chapter 16.

                      -

                      Transfer learning

                      +

                      Transfer learning

                      The goal of transfer learning is to transfer the model or knowledge @@ -1511,7 +1594,7 @@ research topic in recent years, with many problems still waiting to be studied.

                      -

                      Adversarial learning

                      +

                      Adversarial learning

                      The conventional deep generative model has a potential problem: the @@ -1530,7 +1613,7 @@ successfully applied to image, speech, and text.

                      -

                      Dual learning

                      +

                      Dual learning

                      Dual learning is a new learning paradigm, the basic idea of which is @@ -1546,7 +1629,7 @@ image-to-text, and text-to-image.

                      -

                      Distributed machine learning

                      +

                      Distributed machine learning

                      Distributed computation will speed up machine learning algorithms, @@ -1557,7 +1640,7 @@ implementing the machine learning algorithms in parallel is required.

                      -

                      Meta learning

                      +

                      Meta learning

                      Meta learning is an emerging research direction in machine @@ -1571,7 +1654,7 @@ tasks.

                      -

                      The Challenges Facing Machine Learning

                      +

                      The Challenges Facing Machine Learning

                      While there has been much progress in machine learning, there are also challenges. @@ -1596,7 +1679,7 @@ the next ten years will be.

                      -

                      Explainable machine learning

                      +

                      Explainable machine learning

                      Machine learning, especially deep learning, evolves rapidly. The @@ -1621,7 +1704,7 @@ problems by logical reasoning. Bayesian Machine Learning is one of the exciting

                      -

                      Quantum machine learning

                      +

                      Quantum machine learning

                      Quantum machine learning is an emerging interdisciplinary research @@ -1652,7 +1735,7 @@ computing systems.

                      -

                      Quantum machine learning algorithms based on linear algebra

                      +

                      Quantum machine learning algorithms based on linear algebra

                      Many quantum machine learning algorithms are based on variants of @@ -1671,7 +1754,7 @@ input data into a quantum system is as yet unknown for most cases.

                      -

                      Quantum reinforcement learning

                      +

                      Quantum reinforcement learning

                      In quantum reinforcement learning, a quantum agent interacts with the @@ -1685,7 +1768,7 @@ superconducting circuits and systems of trapped ions.

                      -

                      Quantum deep learning

                      +

                      Quantum deep learning

                      Dedicated quantum information processors, such as quantum annealers @@ -1704,7 +1787,7 @@ result.

                      -

                      Social machine learning

                      +

                      Social machine learning

                      Machine learning aims to imitate how humans @@ -1722,7 +1805,7 @@ And much more.

                      -

                      The last words?

                      +

                      The last words?

                      Early computer scientist Alan Kay said, The best way to predict the @@ -1734,7 +1817,7 @@ topics. Together, we will not just predict the future, but create it.

                      -

                      Best wishes to you all and thanks so much for your heroic efforts this semester

                      +

                      Best wishes to you all and thanks so much for your heroic efforts this semester





                      diff --git a/doc/pub/week48/html/week48-solarized.html b/doc/pub/week48/html/week48-solarized.html index 10b838e36..873e0e3b9 100644 --- a/doc/pub/week48/html/week48-solarized.html +++ b/doc/pub/week48/html/week48-solarized.html @@ -68,87 +68,101 @@ div { text-align: justify; text-justify: inter-word; } ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -190,7 +204,7 @@ MathJax.Hub.Config({
                      [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

                      -

                      Nov 25, 2020

                      +

                      Nov 26, 2020












                      @@ -264,13 +278,13 @@ wavelets, splines etc.

                      If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +here generated by the code below (see also Figures 12.2 and 12.3 of Hastie et al.), we can achieve a better separation by introducing more complex +basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to obtain a separation between the classes which is almost linear.

                      The change of basis, from \( x\rightarrow z=\phi(x) \) leads to the same type of equations to be solved, except that -we need to introduce for example a polynomial transformation to a two-dimensional training set. +we need to introduce, for example, a polynomial transformation to a two-dimensional training set.

                      @@ -330,7 +344,7 @@ plt.show()

                      Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables) $$ -z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right). +z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right). $$

                      @@ -341,7 +355,7 @@ $$ subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \), and for the support vectors $$ -y_i(\boldsymbol{w}^T\boldsymbol{z}_i+b)= 1 \hspace{0.1cm}\forall i, +y_i(\boldsymbol{z}_i^T\boldsymbol{w}+b)= 1 \hspace{0.1cm}\forall i, $$ from which we also find \( b \). @@ -352,26 +366,29 @@ $$ For the above example, the kernel reads $$ -K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2. +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} 1\\ \sqrt{2}x_j \\ \sqrt{2}y_j \\ x_j^2\\ y_i^2\\ \sqrt{2}x_jy_j \end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j. $$

                      -We note that this is nothing but the dot product of the two original -vectors \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). Instead of thus computing the -product in the Lagrangian of \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we simply compute -the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). +We note that this dot product can be rewritten as +$$ +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d, +$$ -

                      +where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \). +To compute the last equation is however inefficient from a computational stand. +Instead of computing the last equation for the kernel, we simply compute +the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). This leads to the so-called -kernel trick and the result leads to the same as if we went through -the trouble of performing the transformation -\( \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j) \) during the SVM calculations. +kernel trick.











                      The problem to solve

                      -Using our definition of the kernel We can rewrite again the Lagrangian + +

                      +Using our definition of the kernel, we can rewrite again the Lagrangian $$ {\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{z}_j, $$ @@ -390,6 +407,11 @@ subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vec \( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). If we add the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \). +

                      +









                      + +

                      Tailoring the equations to the usage of CVXOPT

                      +

                      We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type $$ @@ -406,7 +428,7 @@ Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.











                      -

                      Different kernels and Mercer's theorem

                      +

                      Different kernels and Mercer's theorem

                      There are several popular kernels being used. These are @@ -444,7 +466,7 @@ in practice.











                      -

                      The moons example

                      +

                      The moons example (Adapted from Geron, chapter 5)

                      @@ -640,7 +662,7 @@ plt.show()











                      -

                      Mathematical optimization of convex functions

                      +

                      Mathematical optimization of convex functions

                      A mathematical (quadratic) optimization problem, or just optimization problem, has the form @@ -665,7 +687,7 @@ Convex optimization problems play a central role in applied mathematics and we r











                      -

                      How do we solve these problems?

                      +

                      How do we solve these problems?

                      If we use Python as programming language and wish to venture beyond @@ -686,12 +708,12 @@ The functions we need are contained in the quadratic programming package CVXO import cvxopt

                    -This will make our life much easier. You don't need t write your own optimizer. +This will make our life much easier. You don't need to write your own optimizer.











                    -

                    A simple example

                    +

                    A simple example

                    We remind ourselves about the general problem we want to solve @@ -759,7 +781,7 @@ sol[’primal obj











                    -

                    Back to the more realistic cases

                    +

                    Back to the more realistic cases

                    We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the slack parameter \( C \) we have @@ -779,18 +801,86 @@ With the slack constants this leads to the additional constraint \( 0\leq \lamb











                    -

                    Summary of course

                    +

                    Setting up the matrices and the problem

                    + +

                    +We have the general problem +$$ +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. +\end{align*} +$$ + + +

                      +
                    1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
                      2. +
                    2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
                      3. +
                    3. The \( \boldsymbol{q} \) is zero.
                      4. +
                    4. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
                      5. +
                    5. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into
                      6. +
                    + +\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).











                    -

                    What? Me worry? No final exam in this course!

                    +

                    Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)

                    + +

                    +We have two constraints, \( 0\le \lambda_i \) and \( \lambda_i \le C \). To do this we multiply the ones with the contraint +\( \ge \) with \( -1 \) in order to get \( \le \). It means that the problem \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) +can be written as +$$ +\begin{bmatrix} -1& 0 & 0 & \dots & 0 \\ +0& -1 & 0 & \dots & 0 \\ +0& 0 & -1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & -1 \\ + -& 0 & 0 & \dots & 0 \\ +0& 1 & 0 & \dots & 0 \\ +0& 0 & 1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & 1 \\ +\end{bmatrix}\boldsymbol{\lambda} +\begin{bmatrix} \lambda_1 \\ +\lambda_2 \\ +\lambda_3 \\ +\dots \\ +\lambda_n \\ +\end{bmatrix}\boldsymbol{\lambda}= +\begin{bmatrix} 0 \\ +0 \\ +0 \\ +\dots \\ +0 \\ +C \\ +C \\ +C \\ +\dots \\ +C \\ +\end{bmatrix}\boldsymbol{\lambda} +$$ + +

                    +And then we are ready to go. + +

                    +









                    + +

                    Summary of course

                    + +

                    +









                    + +

                    What? Me worry? No final exam in this course!















                    -

                    Topics we have covered this year

                    +

                    Topics we have covered this year

                    The course has two central parts @@ -802,7 +892,7 @@ The course has two central parts









                    -

                    Statistical analysis and optimization of data

                    +

                    Statistical analysis and optimization of data

                    The following topics be covered @@ -819,7 +909,7 @@ The following topics be covered









                    -

                    Machine learning

                    +

                    Machine learning

                    The following topics will be covered @@ -863,7 +953,7 @@ The following topics will be covered









                    -

                    Learning outcomes and overarching aims of this course

                    +

                    Learning outcomes and overarching aims of this course

                    The course introduces a variety of central algorithms and methods @@ -889,7 +979,7 @@ ethical conduct is emphasized throughout the course.









                    -

                    Perspective on Machine Learning

                    +

                    Perspective on Machine Learning

                    1. Rapidly emerging application area
                      2. @@ -906,7 +996,7 @@ Neural Networks, etc.











                      -

                      Machine Learning Research

                      +

                      Machine Learning Research

                      Where to find recent results: @@ -921,7 +1011,7 @@ Where to find recent results:









                      -

                      Starting your Machine Learning Project

                      +

                      Starting your Machine Learning Project

                      1. Identify problem type: classification, generation, regression
                        2. @@ -933,7 +1023,7 @@ Where to find recent results:









                        -

                        Choose a Model and Algorithm

                        +

                        Choose a Model and Algorithm

                        1. Supervised?
                          2. @@ -943,7 +1033,7 @@ Where to find recent results:









                          -

                          Preparing Your Data

                          +

                          Preparing Your Data

                          1. Shuffle your data
                            2. @@ -971,7 +1061,7 @@ Where to find recent results:









                            -

                            Which Activation and Weights to Choose in Neural Networks

                            +

                            Which Activation and Weights to Choose in Neural Networks

                            1. RELU? ELU?
                              2. @@ -992,7 +1082,7 @@ Where to find recent results:









                              -

                              Optimization Methods and Hyperparameters

                              +

                              Optimization Methods and Hyperparameters

                              1. Stochastic gradient descent @@ -1015,7 +1105,7 @@ Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifie











                                -

                                Resampling

                                +

                                Resampling

                                When do we resample? @@ -1028,7 +1118,7 @@ When do we resample?









                                -

                                Other courses on Data science and Machine Learning at UiO

                                +

                                Other courses on Data science and Machine Learning at UiO

                                The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/ gives an excellent overview of courses on Machine learning at UiO. @@ -1046,7 +1136,7 @@ The link here Additional courses of interest +

                                Additional courses of interest

                                1. STK4051 Computational Statistics
                                  2. @@ -1055,7 +1145,7 @@ The link here What's the future like? +

                                  What's the future like?

                                  Based on multi-layer nonlinear neural networks, deep learning can @@ -1078,7 +1168,7 @@ networks have been proposed, such as









                                  -

                                  Types of Machine Learning, a repetition

                                  +

                                  Types of Machine Learning, a repetition

                                  @@ -1108,7 +1198,7 @@ Some of the most common tasks are:











                                  -

                                  Why Boltzmann machines?

                                  +

                                  Why Boltzmann machines?

                                  What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. @@ -1123,7 +1213,7 @@ Furthermore, they have been used to solve complicated Boltzmann Machines +

                                  Boltzmann Machines

                                  Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? @@ -1142,7 +1232,7 @@ Why use a generative model rather than the more well known discriminative deep n









                                  -

                                  Some similarities and differences from DNNs

                                  +

                                  Some similarities and differences from DNNs

                                  1. Both use gradient-descent based learning procedures for minimizing cost functions
                                    2. @@ -1155,7 +1245,7 @@ History: The RBM was developed by amongst others                                     Boltzmann machines (BM) +

                                    Boltzmann machines (BM)

                                    @@ -1187,7 +1277,7 @@ the learned distribution.











                                    -

                                    A standard BM setup

                                    +

                                    A standard BM setup

                                    @@ -1220,7 +1310,7 @@ Here we take away all lateral connections between nodes in the visible layer as











                                    -

                                    The structure of the RBM network

                                    +

                                    The structure of the RBM network





                                    @@ -1228,7 +1318,7 @@ Here we take away all lateral connections between nodes in the visible layer as











                                    -

                                    The network

                                    +

                                    The network

                                    The network layers: @@ -1240,7 +1330,7 @@ Here we take away all lateral connections between nodes in the visible layer as









                                    -

                                    Goals

                                    +

                                    Goals

                                    The goal of the hidden layer is to increase the model's expressive @@ -1261,7 +1351,7 @@ over (integrated out).









                                    -

                                    Joint distribution

                                    +

                                    Joint distribution

                                    The restricted Boltzmann machine is described by a Bolztmann distribution @@ -1285,7 +1375,7 @@ It is common to ignore \( T_0 \) by setting it to one.











                                    -

                                    Network Elements, the energy function

                                    +

                                    Network Elements, the energy function

                                    The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a @@ -1313,7 +1403,7 @@ The connection between the nodes in the two layers is given by the weights \( w_











                                    -

                                    Defining different types of RBMs

                                    +

                                    Defining different types of RBMs

                                    There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function \( E(\mathbf{x},\mathbf{h}) \).

                                    @@ -1351,7 +1441,7 @@ $$











                                    -

                                    More about RBMs

                                    +

                                    More about RBMs

                                    1. Useful when we model continuous data (i.e., we wish \( \mathbf{x} \) to be continuous)
                                      2. @@ -1369,7 +1459,7 @@ Other types of units include:









                                      -

                                      Autoencoders: Overarching view

                                      +

                                      Autoencoders: Overarching view

                                      Autoencoders are artificial neural networks capable of learning @@ -1407,7 +1497,7 @@ See also A. Geron's textbook, chapter 15.











                                      -

                                      Bayesian Machine Learning

                                      +

                                      Bayesian Machine Learning

                                      This is an important topic if we aim at extracting a probability @@ -1429,7 +1519,7 @@ See also the Reinforcement Learning +

                                      Reinforcement Learning

                                      Reinforcement Learning (RL) is one of the most exciting fields of @@ -1463,7 +1553,7 @@ learning. See also A. Geron's textbook, chapter 16.









                                      -

                                      Transfer learning

                                      +

                                      Transfer learning

                                      The goal of transfer learning is to transfer the model or knowledge @@ -1481,7 +1571,7 @@ research topic in recent years, with many problems still waiting to be studied.











                                      -

                                      Adversarial learning

                                      +

                                      Adversarial learning

                                      The conventional deep generative model has a potential problem: the @@ -1500,7 +1590,7 @@ successfully applied to image, speech, and text.











                                      -

                                      Dual learning

                                      +

                                      Dual learning

                                      Dual learning is a new learning paradigm, the basic idea of which is @@ -1516,7 +1606,7 @@ image-to-text, and text-to-image.











                                      -

                                      Distributed machine learning

                                      +

                                      Distributed machine learning

                                      Distributed computation will speed up machine learning algorithms, @@ -1527,7 +1617,7 @@ implementing the machine learning algorithms in parallel is required.











                                      -

                                      Meta learning

                                      +

                                      Meta learning

                                      Meta learning is an emerging research direction in machine @@ -1541,7 +1631,7 @@ tasks.











                                      -

                                      The Challenges Facing Machine Learning

                                      +

                                      The Challenges Facing Machine Learning

                                      While there has been much progress in machine learning, there are also challenges. @@ -1566,7 +1656,7 @@ the next ten years will be.











                                      -

                                      Explainable machine learning

                                      +

                                      Explainable machine learning

                                      Machine learning, especially deep learning, evolves rapidly. The @@ -1591,7 +1681,7 @@ problems by logical reasoning. Bayesian Machine Learning is one of the exciting











                                      -

                                      Quantum machine learning

                                      +

                                      Quantum machine learning

                                      Quantum machine learning is an emerging interdisciplinary research @@ -1622,7 +1712,7 @@ computing systems.











                                      -

                                      Quantum machine learning algorithms based on linear algebra

                                      +

                                      Quantum machine learning algorithms based on linear algebra

                                      Many quantum machine learning algorithms are based on variants of @@ -1641,7 +1731,7 @@ input data into a quantum system is as yet unknown for most cases.











                                      -

                                      Quantum reinforcement learning

                                      +

                                      Quantum reinforcement learning

                                      In quantum reinforcement learning, a quantum agent interacts with the @@ -1655,7 +1745,7 @@ superconducting circuits and systems of trapped ions.











                                      -

                                      Quantum deep learning

                                      +

                                      Quantum deep learning

                                      Dedicated quantum information processors, such as quantum annealers @@ -1674,7 +1764,7 @@ result.











                                      -

                                      Social machine learning

                                      +

                                      Social machine learning

                                      Machine learning aims to imitate how humans @@ -1692,7 +1782,7 @@ And much more.











                                      -

                                      The last words?

                                      +

                                      The last words?

                                      Early computer scientist Alan Kay said, The best way to predict the @@ -1704,7 +1794,7 @@ topics. Together, we will not just predict the future, but create it.











                                      -

                                      Best wishes to you all and thanks so much for your heroic efforts this semester

                                      +

                                      Best wishes to you all and thanks so much for your heroic efforts this semester





                                      diff --git a/doc/pub/week48/html/week48.html b/doc/pub/week48/html/week48.html index 2b6701145..2b26fdf3d 100644 --- a/doc/pub/week48/html/week48.html +++ b/doc/pub/week48/html/week48.html @@ -73,87 +73,101 @@ div { text-align: justify; text-justify: inter-word; } ('Kernels and non-linearity', 2, None, '___sec4'), ('The equations', 2, None, '___sec5'), ('The problem to solve', 2, None, '___sec6'), - ("Different kernels and Mercer's theorem", 2, None, '___sec7'), - ('The moons example', 2, None, '___sec8'), - ('Mathematical optimization of convex functions', + ('Tailoring the equations to the usage of CVXOPT', + 2, + None, + '___sec7'), + ("Different kernels and Mercer's theorem", 2, None, '___sec8'), + ('The moons example ("Adapted from Geron, chapter ' + '5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/")', 2, None, '___sec9'), - ('How do we solve these problems?', 2, None, '___sec10'), - ('A simple example', 2, None, '___sec11'), - ('Back to the more realistic cases', 2, None, '___sec12'), - ('Summary of course', 2, None, '___sec13'), + ('Mathematical optimization of convex functions', + 2, + None, + '___sec10'), + ('How do we solve these problems?', 2, None, '___sec11'), + ('A simple example', 2, None, '___sec12'), + ('Back to the more realistic cases', 2, None, '___sec13'), + ('Setting up the matrices and the problem', 2, None, '___sec14'), + ('Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq ' + '\\boldsymbol{h}$', + 2, + None, + '___sec15'), + ('Summary of course', 2, None, '___sec16'), ('What? Me worry? No final exam in this course!', 2, None, - '___sec14'), - ('Topics we have covered this year', 2, None, '___sec15'), + '___sec17'), + ('Topics we have covered this year', 2, None, '___sec18'), ('Statistical analysis and optimization of data', 2, None, - '___sec16'), - ('Machine learning', 2, None, '___sec17'), + '___sec19'), + ('Machine learning', 2, None, '___sec20'), ('Learning outcomes and overarching aims of this course', 2, None, - '___sec18'), - ('Perspective on Machine Learning', 2, None, '___sec19'), - ('Machine Learning Research', 2, None, '___sec20'), - ('Starting your Machine Learning Project', 2, None, '___sec21'), - ('Choose a Model and Algorithm', 2, None, '___sec22'), - ('Preparing Your Data', 2, None, '___sec23'), + '___sec21'), + ('Perspective on Machine Learning', 2, None, '___sec22'), + ('Machine Learning Research', 2, None, '___sec23'), + ('Starting your Machine Learning Project', 2, None, '___sec24'), + ('Choose a Model and Algorithm', 2, None, '___sec25'), + ('Preparing Your Data', 2, None, '___sec26'), ('Which Activation and Weights to Choose in Neural Networks', 2, None, - '___sec24'), - ('Optimization Methods and Hyperparameters', 2, None, '___sec25'), - ('Resampling', 2, None, '___sec26'), + '___sec27'), + ('Optimization Methods and Hyperparameters', 2, None, '___sec28'), + ('Resampling', 2, None, '___sec29'), ('Other courses on Data science and Machine Learning at UiO', 2, None, - '___sec27'), - ('Additional courses of interest', 2, None, '___sec28'), - ("What's the future like?", 2, None, '___sec29'), - ('Types of Machine Learning, a repetition', 2, None, '___sec30'), - ('Why Boltzmann machines?', 2, None, '___sec31'), - ('Boltzmann Machines', 2, None, '___sec32'), + '___sec30'), + ('Additional courses of interest', 2, None, '___sec31'), + ("What's the future like?", 2, None, '___sec32'), + ('Types of Machine Learning, a repetition', 2, None, '___sec33'), + ('Why Boltzmann machines?', 2, None, '___sec34'), + ('Boltzmann Machines', 2, None, '___sec35'), ('Some similarities and differences from DNNs', 2, None, - '___sec33'), - ('Boltzmann machines (BM)', 2, None, '___sec34'), - ('A standard BM setup', 2, None, '___sec35'), - ('The structure of the RBM network', 2, None, '___sec36'), - ('The network', 2, None, '___sec37'), - ('Goals', 2, None, '___sec38'), - ('Joint distribution', 2, None, '___sec39'), - ('Network Elements, the energy function', 2, None, '___sec40'), - ('Defining different types of RBMs', 2, None, '___sec41'), - ('More about RBMs', 2, None, '___sec42'), - ('Autoencoders: Overarching view', 2, None, '___sec43'), - ('Bayesian Machine Learning', 2, None, '___sec44'), - ('Reinforcement Learning', 2, None, '___sec45'), - ('Transfer learning', 2, None, '___sec46'), - ('Adversarial learning', 2, None, '___sec47'), - ('Dual learning', 2, None, '___sec48'), - ('Distributed machine learning', 2, None, '___sec49'), - ('Meta learning', 2, None, '___sec50'), - ('The Challenges Facing Machine Learning', 2, None, '___sec51'), - ('Explainable machine learning', 2, None, '___sec52'), - ('Quantum machine learning', 2, None, '___sec53'), + '___sec36'), + ('Boltzmann machines (BM)', 2, None, '___sec37'), + ('A standard BM setup', 2, None, '___sec38'), + ('The structure of the RBM network', 2, None, '___sec39'), + ('The network', 2, None, '___sec40'), + ('Goals', 2, None, '___sec41'), + ('Joint distribution', 2, None, '___sec42'), + ('Network Elements, the energy function', 2, None, '___sec43'), + ('Defining different types of RBMs', 2, None, '___sec44'), + ('More about RBMs', 2, None, '___sec45'), + ('Autoencoders: Overarching view', 2, None, '___sec46'), + ('Bayesian Machine Learning', 2, None, '___sec47'), + ('Reinforcement Learning', 2, None, '___sec48'), + ('Transfer learning', 2, None, '___sec49'), + ('Adversarial learning', 2, None, '___sec50'), + ('Dual learning', 2, None, '___sec51'), + ('Distributed machine learning', 2, None, '___sec52'), + ('Meta learning', 2, None, '___sec53'), + ('The Challenges Facing Machine Learning', 2, None, '___sec54'), + ('Explainable machine learning', 2, None, '___sec55'), + ('Quantum machine learning', 2, None, '___sec56'), ('Quantum machine learning algorithms based on linear algebra', 2, None, - '___sec54'), - ('Quantum reinforcement learning', 2, None, '___sec55'), - ('Quantum deep learning', 2, None, '___sec56'), - ('Social machine learning', 2, None, '___sec57'), - ('The last words?', 2, None, '___sec58'), + '___sec57'), + ('Quantum reinforcement learning', 2, None, '___sec58'), + ('Quantum deep learning', 2, None, '___sec59'), + ('Social machine learning', 2, None, '___sec60'), + ('The last words?', 2, None, '___sec61'), ('Best wishes to you all and thanks so much for your heroic ' 'efforts this semester', 2, None, - '___sec59')]} + '___sec62')]} end of tocinfo --> @@ -195,7 +209,7 @@ MathJax.Hub.Config({
                                      [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

                                      -

                                      Nov 25, 2020

                                      +

                                      Nov 26, 2020












                                      @@ -269,13 +283,13 @@ wavelets, splines etc.

                                      If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +here generated by the code below (see also Figures 12.2 and 12.3 of Hastie et al.), we can achieve a better separation by introducing more complex +basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to obtain a separation between the classes which is almost linear.

                                      The change of basis, from \( x\rightarrow z=\phi(x) \) leads to the same type of equations to be solved, except that -we need to introduce for example a polynomial transformation to a two-dimensional training set. +we need to introduce, for example, a polynomial transformation to a two-dimensional training set.

                                      @@ -335,7 +349,7 @@ plt.show()

                                      Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables) $$ -z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right). +z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right). $$

                                      @@ -346,7 +360,7 @@ $$ subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \), and for the support vectors $$ -y_i(\boldsymbol{w}^T\boldsymbol{z}_i+b)= 1 \hspace{0.1cm}\forall i, +y_i(\boldsymbol{z}_i^T\boldsymbol{w}+b)= 1 \hspace{0.1cm}\forall i, $$ from which we also find \( b \). @@ -357,26 +371,29 @@ $$ For the above example, the kernel reads $$ -K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2. +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} 1\\ \sqrt{2}x_j \\ \sqrt{2}y_j \\ x_j^2\\ y_i^2\\ \sqrt{2}x_jy_j \end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j. $$

                                      -We note that this is nothing but the dot product of the two original -vectors \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). Instead of thus computing the -product in the Lagrangian of \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we simply compute -the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). +We note that this dot product can be rewritten as +$$ +K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d, +$$ -

                                      +where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \). +To compute the last equation is however inefficient from a computational stand. +Instead of computing the last equation for the kernel, we simply compute +the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). This leads to the so-called -kernel trick and the result leads to the same as if we went through -the trouble of performing the transformation -\( \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j) \) during the SVM calculations. +kernel trick.











                                      The problem to solve

                                      -Using our definition of the kernel We can rewrite again the Lagrangian + +

                                      +Using our definition of the kernel, we can rewrite again the Lagrangian $$ {\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{z}_j, $$ @@ -395,6 +412,11 @@ subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vec \( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \). If we add the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \). +

                                      +









                                      + +

                                      Tailoring the equations to the usage of CVXOPT

                                      +

                                      We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type $$ @@ -411,7 +433,7 @@ Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.











                                      -

                                      Different kernels and Mercer's theorem

                                      +

                                      Different kernels and Mercer's theorem

                                      There are several popular kernels being used. These are @@ -449,7 +471,7 @@ in practice.











                                      -

                                      The moons example

                                      +

                                      The moons example (Adapted from Geron, chapter 5)

                                      @@ -645,7 +667,7 @@ plt.show()











                                      -

                                      Mathematical optimization of convex functions

                                      +

                                      Mathematical optimization of convex functions

                                      A mathematical (quadratic) optimization problem, or just optimization problem, has the form @@ -670,7 +692,7 @@ Convex optimization problems play a central role in applied mathematics and we r











                                      -

                                      How do we solve these problems?

                                      +

                                      How do we solve these problems?

                                      If we use Python as programming language and wish to venture beyond @@ -691,12 +713,12 @@ The functions we need are contained in the quadratic programming package CVXO import cvxopt

                                    -This will make our life much easier. You don't need t write your own optimizer. +This will make our life much easier. You don't need to write your own optimizer.











                                    -

                                    A simple example

                                    +

                                    A simple example

                                    We remind ourselves about the general problem we want to solve @@ -764,7 +786,7 @@ sol[’primal objective’]











                                    -

                                    Back to the more realistic cases

                                    +

                                    Back to the more realistic cases

                                    We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the slack parameter \( C \) we have @@ -784,18 +806,86 @@ With the slack constants this leads to the additional constraint \( 0\leq \lamb











                                    -

                                    Summary of course

                                    +

                                    Setting up the matrices and the problem

                                    + +

                                    +We have the general problem +$$ +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. +\end{align*} +$$ + + +

                                      +
                                    1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
                                      2. +
                                    2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
                                      3. +
                                    3. The \( \boldsymbol{q} \) is zero.
                                      4. +
                                    4. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
                                      5. +
                                    5. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into
                                      6. +
                                    + +\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).











                                    -

                                    What? Me worry? No final exam in this course!

                                    +

                                    Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \)

                                    + +

                                    +We have two constraints, \( 0\le \lambda_i \) and \( \lambda_i \le C \). To do this we multiply the ones with the contraint +\( \ge \) with \( -1 \) in order to get \( \le \). It means that the problem \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) +can be written as +$$ +\begin{bmatrix} -1& 0 & 0 & \dots & 0 \\ +0& -1 & 0 & \dots & 0 \\ +0& 0 & -1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & -1 \\ + -& 0 & 0 & \dots & 0 \\ +0& 1 & 0 & \dots & 0 \\ +0& 0 & 1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & 1 \\ +\end{bmatrix}\boldsymbol{\lambda} +\begin{bmatrix} \lambda_1 \\ +\lambda_2 \\ +\lambda_3 \\ +\dots \\ +\lambda_n \\ +\end{bmatrix}\boldsymbol{\lambda}= +\begin{bmatrix} 0 \\ +0 \\ +0 \\ +\dots \\ +0 \\ +C \\ +C \\ +C \\ +\dots \\ +C \\ +\end{bmatrix}\boldsymbol{\lambda} +$$ + +

                                    +And then we are ready to go. + +

                                    +









                                    + +

                                    Summary of course

                                    + +

                                    +









                                    + +

                                    What? Me worry? No final exam in this course!















                                    -

                                    Topics we have covered this year

                                    +

                                    Topics we have covered this year

                                    The course has two central parts @@ -807,7 +897,7 @@ The course has two central parts









                                    -

                                    Statistical analysis and optimization of data

                                    +

                                    Statistical analysis and optimization of data

                                    The following topics be covered @@ -824,7 +914,7 @@ The following topics be covered









                                    -

                                    Machine learning

                                    +

                                    Machine learning

                                    The following topics will be covered @@ -868,7 +958,7 @@ The following topics will be covered









                                    -

                                    Learning outcomes and overarching aims of this course

                                    +

                                    Learning outcomes and overarching aims of this course

                                    The course introduces a variety of central algorithms and methods @@ -894,7 +984,7 @@ ethical conduct is emphasized throughout the course.









                                    -

                                    Perspective on Machine Learning

                                    +

                                    Perspective on Machine Learning

                                    1. Rapidly emerging application area
                                      2. @@ -911,7 +1001,7 @@ Neural Networks, etc.











                                      -

                                      Machine Learning Research

                                      +

                                      Machine Learning Research

                                      Where to find recent results: @@ -926,7 +1016,7 @@ Where to find recent results:









                                      -

                                      Starting your Machine Learning Project

                                      +

                                      Starting your Machine Learning Project

                                      1. Identify problem type: classification, generation, regression
                                        2. @@ -938,7 +1028,7 @@ Where to find recent results:









                                        -

                                        Choose a Model and Algorithm

                                        +

                                        Choose a Model and Algorithm

                                        1. Supervised?
                                          2. @@ -948,7 +1038,7 @@ Where to find recent results:









                                          -

                                          Preparing Your Data

                                          +

                                          Preparing Your Data

                                          1. Shuffle your data
                                            2. @@ -976,7 +1066,7 @@ Where to find recent results:









                                            -

                                            Which Activation and Weights to Choose in Neural Networks

                                            +

                                            Which Activation and Weights to Choose in Neural Networks

                                            1. RELU? ELU?
                                              2. @@ -997,7 +1087,7 @@ Where to find recent results:









                                              -

                                              Optimization Methods and Hyperparameters

                                              +

                                              Optimization Methods and Hyperparameters

                                              1. Stochastic gradient descent @@ -1020,7 +1110,7 @@ Which regularization and hyperparameters? \( L_1 \) or \( L_2 \), soft classifie











                                                -

                                                Resampling

                                                +

                                                Resampling

                                                When do we resample? @@ -1033,7 +1123,7 @@ When do we resample?









                                                -

                                                Other courses on Data science and Machine Learning at UiO

                                                +

                                                Other courses on Data science and Machine Learning at UiO

                                                The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/ gives an excellent overview of courses on Machine learning at UiO. @@ -1051,7 +1141,7 @@ The link here Additional courses of interest +

                                                Additional courses of interest

                                                1. STK4051 Computational Statistics
                                                  2. @@ -1060,7 +1150,7 @@ The link here What's the future like? +

                                                  What's the future like?

                                                  Based on multi-layer nonlinear neural networks, deep learning can @@ -1083,7 +1173,7 @@ networks have been proposed, such as









                                                  -

                                                  Types of Machine Learning, a repetition

                                                  +

                                                  Types of Machine Learning, a repetition

                                                  @@ -1113,7 +1203,7 @@ Some of the most common tasks are:











                                                  -

                                                  Why Boltzmann machines?

                                                  +

                                                  Why Boltzmann machines?

                                                  What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. @@ -1128,7 +1218,7 @@ Furthermore, they have been used to solve complicated Boltzmann Machines +

                                                  Boltzmann Machines

                                                  Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? @@ -1147,7 +1237,7 @@ Why use a generative model rather than the more well known discriminative deep n









                                                  -

                                                  Some similarities and differences from DNNs

                                                  +

                                                  Some similarities and differences from DNNs

                                                  1. Both use gradient-descent based learning procedures for minimizing cost functions
                                                    2. @@ -1160,7 +1250,7 @@ History: The RBM was developed by amongst others                                                     Boltzmann machines (BM) +

                                                    Boltzmann machines (BM)

                                                    @@ -1192,7 +1282,7 @@ the learned distribution.











                                                    -

                                                    A standard BM setup

                                                    +

                                                    A standard BM setup

                                                    @@ -1225,7 +1315,7 @@ Here we take away all lateral connections between nodes in the visible layer as











                                                    -

                                                    The structure of the RBM network

                                                    +

                                                    The structure of the RBM network





                                                    @@ -1233,7 +1323,7 @@ Here we take away all lateral connections between nodes in the visible layer as











                                                    -

                                                    The network

                                                    +

                                                    The network

                                                    The network layers: @@ -1245,7 +1335,7 @@ Here we take away all lateral connections between nodes in the visible layer as









                                                    -

                                                    Goals

                                                    +

                                                    Goals

                                                    The goal of the hidden layer is to increase the model's expressive @@ -1266,7 +1356,7 @@ over (integrated out).









                                                    -

                                                    Joint distribution

                                                    +

                                                    Joint distribution

                                                    The restricted Boltzmann machine is described by a Bolztmann distribution @@ -1290,7 +1380,7 @@ It is common to ignore \( T_0 \) by setting it to one.











                                                    -

                                                    Network Elements, the energy function

                                                    +

                                                    Network Elements, the energy function

                                                    The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a @@ -1318,7 +1408,7 @@ The connection between the nodes in the two layers is given by the weights \( w_











                                                    -

                                                    Defining different types of RBMs

                                                    +

                                                    Defining different types of RBMs

                                                    There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function \( E(\mathbf{x},\mathbf{h}) \).

                                                    @@ -1356,7 +1446,7 @@ $$











                                                    -

                                                    More about RBMs

                                                    +

                                                    More about RBMs

                                                    1. Useful when we model continuous data (i.e., we wish \( \mathbf{x} \) to be continuous)
                                                      2. @@ -1374,7 +1464,7 @@ Other types of units include:









                                                      -

                                                      Autoencoders: Overarching view

                                                      +

                                                      Autoencoders: Overarching view

                                                      Autoencoders are artificial neural networks capable of learning @@ -1412,7 +1502,7 @@ See also A. Geron's textbook, chapter 15.











                                                      -

                                                      Bayesian Machine Learning

                                                      +

                                                      Bayesian Machine Learning

                                                      This is an important topic if we aim at extracting a probability @@ -1434,7 +1524,7 @@ See also the Reinforcement Learning +

                                                      Reinforcement Learning

                                                      Reinforcement Learning (RL) is one of the most exciting fields of @@ -1468,7 +1558,7 @@ learning. See also A. Geron's textbook, chapter 16.









                                                      -

                                                      Transfer learning

                                                      +

                                                      Transfer learning

                                                      The goal of transfer learning is to transfer the model or knowledge @@ -1486,7 +1576,7 @@ research topic in recent years, with many problems still waiting to be studied.











                                                      -

                                                      Adversarial learning

                                                      +

                                                      Adversarial learning

                                                      The conventional deep generative model has a potential problem: the @@ -1505,7 +1595,7 @@ successfully applied to image, speech, and text.











                                                      -

                                                      Dual learning

                                                      +

                                                      Dual learning

                                                      Dual learning is a new learning paradigm, the basic idea of which is @@ -1521,7 +1611,7 @@ image-to-text, and text-to-image.











                                                      -

                                                      Distributed machine learning

                                                      +

                                                      Distributed machine learning

                                                      Distributed computation will speed up machine learning algorithms, @@ -1532,7 +1622,7 @@ implementing the machine learning algorithms in parallel is required.











                                                      -

                                                      Meta learning

                                                      +

                                                      Meta learning

                                                      Meta learning is an emerging research direction in machine @@ -1546,7 +1636,7 @@ tasks.











                                                      -

                                                      The Challenges Facing Machine Learning

                                                      +

                                                      The Challenges Facing Machine Learning

                                                      While there has been much progress in machine learning, there are also challenges. @@ -1571,7 +1661,7 @@ the next ten years will be.











                                                      -

                                                      Explainable machine learning

                                                      +

                                                      Explainable machine learning

                                                      Machine learning, especially deep learning, evolves rapidly. The @@ -1596,7 +1686,7 @@ problems by logical reasoning. Bayesian Machine Learning is one of the exciting











                                                      -

                                                      Quantum machine learning

                                                      +

                                                      Quantum machine learning

                                                      Quantum machine learning is an emerging interdisciplinary research @@ -1627,7 +1717,7 @@ computing systems.











                                                      -

                                                      Quantum machine learning algorithms based on linear algebra

                                                      +

                                                      Quantum machine learning algorithms based on linear algebra

                                                      Many quantum machine learning algorithms are based on variants of @@ -1646,7 +1736,7 @@ input data into a quantum system is as yet unknown for most cases.











                                                      -

                                                      Quantum reinforcement learning

                                                      +

                                                      Quantum reinforcement learning

                                                      In quantum reinforcement learning, a quantum agent interacts with the @@ -1660,7 +1750,7 @@ superconducting circuits and systems of trapped ions.











                                                      -

                                                      Quantum deep learning

                                                      +

                                                      Quantum deep learning

                                                      Dedicated quantum information processors, such as quantum annealers @@ -1679,7 +1769,7 @@ result.











                                                      -

                                                      Social machine learning

                                                      +

                                                      Social machine learning

                                                      Machine learning aims to imitate how humans @@ -1697,7 +1787,7 @@ And much more.











                                                      -

                                                      The last words?

                                                      +

                                                      The last words?

                                                      Early computer scientist Alan Kay said, The best way to predict the @@ -1709,7 +1799,7 @@ topics. Together, we will not just predict the future, but create it.











                                                      -

                                                      Best wishes to you all and thanks so much for your heroic efforts this semester

                                                      +

                                                      Best wishes to you all and thanks so much for your heroic efforts this semester





                                                      diff --git a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz index f82be520dec74f6e55a3a040c882776739ae76f4..3adffd0501062b77f0d11fb5f234538b900007f6 100644 GIT binary patch delta 54 zcmaDg%jnfCBX;?24u)wC`y1I?*%@2enOfPITiID!*;!lJ*;?6wf*h^voUQC!t?b-e I*?E$C0lps&K>z>% delta 54 zcmaDg%jnfCBX;?24hAW;eU0p`?2N7KOs(w9t?VqV?5wTqY_04-L5@~-&Q^A=R(9^K I>^#Z60HodxssI20 diff --git a/doc/pub/week48/ipynb/week48.ipynb b/doc/pub/week48/ipynb/week48.ipynb index 8f3b41c5e..65b1ea189 100644 --- a/doc/pub/week48/ipynb/week48.ipynb +++ b/doc/pub/week48/ipynb/week48.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Nov 25, 2020**\n", + "Date: **Nov 26, 2020**\n", "\n", "Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -66,12 +66,12 @@ "wavelets, splines etc.\n", "\n", "If our feature space is not easy to separate, as shown in the figure\n", - "here, we can achieve a better separation by introducing more complex\n", - "basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to \n", + "here generated by the code below (see also Figures 12.2 and 12.3 of [Hastie et al.](https://www.springer.com/gp/book/9780387848570)), we can achieve a better separation by introducing more complex\n", + "basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to \n", "obtain a separation between the classes which is almost linear. \n", "\n", "The change of basis, from $x\\rightarrow z=\\phi(x)$ leads to the same type of equations to be solved, except that\n", - "we need to introduce for example a polynomial transformation to a two-dimensional training set." + "we need to introduce, for example, a polynomial transformation to a two-dimensional training set." ] }, { @@ -146,7 +146,7 @@ "metadata": {}, "source": [ "$$\n", - "z = \\phi(x_i) =\\left(x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n", + "z = \\phi(x_i) =\\left(1, \\sqrt{2}x_i, \\sqrt{2}y_i, x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n", "$$" ] }, @@ -178,7 +178,7 @@ "metadata": {}, "source": [ "$$\n", - "y_i(\\boldsymbol{w}^T\\boldsymbol{z}_i+b)= 1 \\hspace{0.1cm}\\forall i,\n", + "y_i(\\boldsymbol{z}_i^T\\boldsymbol{w}+b)= 1 \\hspace{0.1cm}\\forall i,\n", "$$" ] }, @@ -211,7 +211,7 @@ "metadata": {}, "source": [ "$$\n", - "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[x_i^2, y_i^2, \\sqrt{2}x_iy_i]^T\\begin{bmatrix} x_j^2 \\\\ y_j^2 \\\\ \\sqrt{2}x_jy_j \\end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2.\n", + "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[1, \\sqrt{2}x_i, \\sqrt{2}y_i, x_i^2, y_i^2, \\sqrt{2}x_iy_i]^T\\begin{bmatrix} 1\\\\ \\sqrt{2}x_j \\\\ \\sqrt{2}y_j \\\\ x_j^2\\\\ y_i^2\\\\ \\sqrt{2}x_jy_j \\end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j.\n", "$$" ] }, @@ -219,20 +219,32 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We note that this is nothing but the dot product of the two original\n", - "vectors $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$. Instead of thus computing the\n", - "product in the Lagrangian of $\\boldsymbol{z}_i^T\\boldsymbol{z}_j$ we simply compute\n", + "We note that this dot product can be rewritten as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[1+\\boldsymbol{x}^T\\boldsymbol{x}']^d,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $d=2$ in our case and $\\boldsymbol{x}=[x_i,y_i]$ and $\\boldsymbol{x}=[x_j,y_j]$.\n", + "To compute the last equation is however inefficient from a computational stand.\n", + "Instead of computing the last equation for the kernel, we simply compute\n", "the dot product $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$.\n", - "\n", - "\n", "This leads to the so-called\n", - "kernel trick and the result leads to the same as if we went through\n", - "the trouble of performing the transformation\n", - "$\\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j)$ during the SVM calculations.\n", - "\n", + "kernel trick.\n", "\n", "## The problem to solve\n", - "Using our definition of the kernel We can rewrite again the Lagrangian" + "\n", + "Using our definition of the kernel, we can rewrite again the Lagrangian" ] }, { @@ -273,6 +285,8 @@ "$\\boldsymbol{y}=[y_1,y_2,\\dots,y_n]$. \n", "If we add the slack constants this leads to the additional constraint $0\\leq \\lambda_i \\leq C$.\n", "\n", + "## Tailoring the equations to the usage of CVXOPT\n", + "\n", "We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type" ] }, @@ -339,7 +353,7 @@ "in practice.\n", "\n", "\n", - "## The moons example" + "## The moons example ([Adapted from Geron, chapter 5](https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/))" ] }, { @@ -605,7 +619,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This will make our life much easier. You don't need t write your own optimizer.\n", + "This will make our life much easier. You don't need to write your own optimizer.\n", "\n", "\n", "## A simple example\n", @@ -776,6 +790,89 @@ "With the slack constants this leads to the additional constraint $0\\leq \\lambda_i \\leq C$.\n", "\n", "\n", + "## Setting up the matrices and the problem\n", + "\n", + "We have the general problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + " &\\mathrm{min}_{\\lambda}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{\\lambda}^T\\boldsymbol{P}\\boldsymbol{\\lambda}+\\boldsymbol{q}^T\\boldsymbol{\\lambda},\\\\ \\nonumber\n", + " &\\mathrm{subject\\hspace{0.1cm}to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. With a given kernel we can thus define the matrix $\\boldsymbol{P}$.\n", + "\n", + "2. The matrix $\\boldsymbol{P}$ has matrix elements $p_{ij}=y_iy_jK(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.\n", + "\n", + "3. The $\\boldsymbol{q}$ is zero.\n", + "\n", + "4. The constraint $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$ leads to $f=0$ and $\\boldsymbol{A}=\\boldsymbol{y}$.\n", + "\n", + "5. To set up the matrix $\\boldsymbol{G}$ we note that the inequalities $0\\leq \\lambda_i \\leq C$ can be split up into\n", + "\n", + "$0\\leq \\lambda_i$ and $\\lambda_i \\leq C$. These two inequalities define then the matrix $\\boldsymbol{G}$ and the vector $\\boldsymbol{h}$.\n", + "\n", + "## Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h}$\n", + "\n", + "We have two constraints, $0\\le \\lambda_i$ and $\\lambda_i \\le C$. To do this we multiply the ones with the contraint\n", + "$\\ge$ with $-1$ in order to get $\\le$. It means that the problem $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h}$\n", + "can be written as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{bmatrix} -1& 0 & 0 & \\dots & 0 \\\\\n", + "0& -1 & 0 & \\dots & 0 \\\\\n", + "0& 0 & -1 & \\dots & 0 \\\\\n", + "\\dots& \\dots & \\dots & \\dots & \\dots \\\\\n", + "0& 0 & 0 & \\dots & -1 \\\\\n", + " -& 0 & 0 & \\dots & 0 \\\\\n", + "0& 1 & 0 & \\dots & 0 \\\\\n", + "0& 0 & 1 & \\dots & 0 \\\\\n", + "\\dots& \\dots & \\dots & \\dots & \\dots \\\\\n", + "0& 0 & 0 & \\dots & 1 \\\\\n", + "\\end{bmatrix}\\boldsymbol{\\lambda}\n", + "\\begin{bmatrix} \\lambda_1 \\\\\n", + "\\lambda_2 \\\\\n", + "\\lambda_3 \\\\\n", + "\\dots \\\\\n", + "\\lambda_n \\\\\n", + "\\end{bmatrix}\\boldsymbol{\\lambda}=\n", + "\\begin{bmatrix} 0 \\\\\n", + "0 \\\\\n", + "0 \\\\\n", + "\\dots \\\\\n", + "0 \\\\\n", + "C \\\\\n", + "C \\\\\n", + "C \\\\\n", + "\\dots \\\\\n", + "C \\\\\n", + "\\end{bmatrix}\\boldsymbol{\\lambda}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then we are ready to go.\n", + "\n", + "\n", "\n", "## Summary of course\n", "\n", diff --git a/doc/src/week48/week48.do.txt b/doc/src/week48/week48.do.txt index dc17c1c00..3209ff18b 100644 --- a/doc/src/week48/week48.do.txt +++ b/doc/src/week48/week48.do.txt @@ -57,12 +57,12 @@ space using other basis expansions such as higher-order polynomials, wavelets, splines etc. If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +here generated by the code below (see also Figures 12.2 and 12.3 of "Hastie et al.":"https://www.springer.com/gp/book/9780387848570"), we can achieve a better separation by introducing more complex +basis functions. The ideal would be (see Figures 12.2 and 12.3) to, via a specific transformation to obtain a separation between the classes which is almost linear. The change of basis, from $x\rightarrow z=\phi(x)$ leads to the same type of equations to be solved, except that -we need to introduce for example a polynomial transformation to a two-dimensional training set. +we need to introduce, for example, a polynomial transformation to a two-dimensional training set. !bc pycod import numpy as np @@ -122,7 +122,7 @@ plt.show() Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables) !bt \[ -z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right). +z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right). \] !et @@ -135,7 +135,7 @@ With our new basis, the equations we solved earlier are basically the same, that subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$, and for the support vectors !bt \[ -y_i(\bm{w}^T\bm{z}_i+b)= 1 \hspace{0.1cm}\forall i, +y_i(\bm{z}_i^T\bm{w}+b)= 1 \hspace{0.1cm}\forall i, \] !et from which we also find $b$. @@ -148,25 +148,27 @@ K(\bm{x}_i,\bm{x}_j)=\bm{z}_i^T\bm{z}_j= \phi(\bm{x}_i)^T\phi(\bm{x}_j). For the above example, the kernel reads !bt \[ -K(\bm{x}_i,\bm{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2. +K(\bm{x}_i,\bm{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} 1\\ \sqrt{2}x_j \\ \sqrt{2}y_j \\ x_j^2\\ y_i^2\\ \sqrt{2}x_jy_j \end{bmatrix}=1+2x_ix_j+2y_iy_j+(x_ix_j)^2+(y_iy_j)^2+2x_ix_jy_iy_j. \] !et -We note that this is nothing but the dot product of the two original -vectors $(\bm{x}_i^T\bm{x}_j)^2$. Instead of thus computing the -product in the Lagrangian of $\bm{z}_i^T\bm{z}_j$ we simply compute +We note that this dot product can be rewritten as +!bt +\[ +K(\bm{x}_i,\bm{x}_j)=[1+\bm{x}^T\bm{x}']^d, +\] +!et +where $d=2$ in our case and $\bm{x}=[x_i,y_i]$ and $\bm{x}=[x_j,y_j]$. +To compute the last equation is however inefficient from a computational stand. +Instead of computing the last equation for the kernel, we simply compute the dot product $(\bm{x}_i^T\bm{x}_j)^2$. - - This leads to the so-called -kernel trick and the result leads to the same as if we went through -the trouble of performing the transformation -$\phi(\bm{x}_i)^T\phi(\bm{x}_j)$ during the SVM calculations. - +kernel trick. !split ===== The problem to solve ===== -Using our definition of the kernel We can rewrite again the Lagrangian + +Using our definition of the kernel, we can rewrite again the Lagrangian !bt \[ {\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\bm{x}_i^T\bm{z}_j, @@ -187,6 +189,9 @@ subject to $\bm{y}^T\bm{\lambda}=0$. Here we defined the vectors $\bm{\lambda} = $\bm{y}=[y_1,y_2,\dots,y_n]$. If we add the slack constants this leads to the additional constraint $0\leq \lambda_i \leq C$. +!split +===== Tailoring the equations to the usage of CVXOPT ===== + We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type !bt \begin{align*} @@ -231,7 +236,7 @@ in practice. !split -===== The moons example ===== +===== The moons example ("Adapted from Geron, chapter 5":"https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/") ===== !bc pycod from __future__ import division, print_function, unicode_literals @@ -465,7 +470,7 @@ import numpy import cvxopt !ec -This will make our life much easier. You don't need t write your own optimizer. +This will make our life much easier. You don't need to write your own optimizer. !split @@ -554,6 +559,68 @@ $\bm{y}=[y_1,y_2,\dots,y_n]$. With the slack constants this leads to the additional constraint $0\leq \lambda_i \leq C$. +!split +===== Setting up the matrices and the problem ===== + +We have the general problem +!bt +\begin{align*} + &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\bm{\lambda}^T\bm{P}\bm{\lambda}+\bm{q}^T\bm{\lambda},\\ \nonumber + &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \wedge \bm{A}\bm{\lambda}=f. +\end{align*} +!et + + + +o With a given kernel we can thus define the matrix $\bm{P}$. +o The matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up. +o The $\bm{q}$ is zero. +o The constraint $\bm{y}^T\bm{\lambda}=0$ leads to $f=0$ and $\bm{A}=\bm{y}$. +o To set up the matrix $\bm{G}$ we note that the inequalities $0\leq \lambda_i \leq C$ can be split up into +$0\leq \lambda_i$ and $\lambda_i \leq C$. These two inequalities define then the matrix $\bm{G}$ and the vector $\bm{h}$. + +!split +===== Setting up $\bm{G}\bm{\lambda} \preceq \bm{h}$ ===== + +We have two constraints, $0\le \lambda_i$ and $\lambda_i \le C$. To do this we multiply the ones with the contraint +$\ge$ with $-1$ in order to get $\le$. It means that the problem $\bm{G}\bm{\lambda} \preceq \bm{h}$ +can be written as +!bt +\[ +\begin{bmatrix} -1& 0 & 0 & \dots & 0 \\ +0& -1 & 0 & \dots & 0 \\ +0& 0 & -1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & -1 \\ + -& 0 & 0 & \dots & 0 \\ +0& 1 & 0 & \dots & 0 \\ +0& 0 & 1 & \dots & 0 \\ +\dots& \dots & \dots & \dots & \dots \\ +0& 0 & 0 & \dots & 1 \\ +\end{bmatrix}\bm{\lambda} +\begin{bmatrix} \lambda_1 \\ +\lambda_2 \\ +\lambda_3 \\ +\dots \\ +\lambda_n \\ +\end{bmatrix}\bm{\lambda}= +\begin{bmatrix} 0 \\ +0 \\ +0 \\ +\dots \\ +0 \\ +C \\ +C \\ +C \\ +\dots \\ +C \\ +\end{bmatrix}\bm{\lambda} +\] +!et + +And then we are ready to go. + + !split ===== Summary of course =====