From 00d4e6e22f8c0d3ec2fa858228b735bdaacc0c27 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Sat, 8 Jun 2019 20:03:19 -0400 Subject: [PATCH] Adding motivation to BNN --- doc/pub/Bayesian/html/._Bayesian-bs000.html | 6 ++-- doc/pub/Bayesian/html/._Bayesian-bs001.html | 32 ++++++++++++------ doc/pub/Bayesian/html/Bayesian-bs.html | 6 ++-- doc/pub/Bayesian/html/Bayesian-reveal.html | 28 +++++++++------ doc/pub/Bayesian/html/Bayesian-solarized.html | 32 ++++++++++++------ doc/pub/Bayesian/html/Bayesian.html | 32 ++++++++++++------ doc/pub/Bayesian/ipynb/Bayesian.ipynb | 22 +++++++----- .../Bayesian/ipynb/ipynb-Bayesian-src.tar.gz | Bin 85220 -> 85220 bytes doc/pub/Bayesian/pdf/Bayesian-minted.pdf | Bin 421291 -> 422027 bytes doc/src/Bayesian/Bayesian.do.txt | 23 +++++++++---- doc/web/course.do.txt | 4 +-- doc/web/course.html | 15 +++++--- 12 files changed, 129 insertions(+), 71 deletions(-) diff --git a/doc/pub/Bayesian/html/._Bayesian-bs000.html b/doc/pub/Bayesian/html/._Bayesian-bs000.html index 426734bac..73bb9265d 100644 --- a/doc/pub/Bayesian/html/._Bayesian-bs000.html +++ b/doc/pub/Bayesian/html/._Bayesian-bs000.html @@ -41,7 +41,7 @@ Automatically generated HTML file from DocOnce source
  • What is Bayesian Statistics
    • +
  • Why Bayesian Statistics?
  • Inference
  • Statistical Inference
  • Some history
    • @@ -175,7 +175,7 @@ MathJax.Hub.Config({
    [3] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Jun 7, 2019

    +

    Jun 8, 2019


    diff --git a/doc/pub/Bayesian/html/._Bayesian-bs001.html b/doc/pub/Bayesian/html/._Bayesian-bs001.html index 94eea8f61..9c7d303a7 100644 --- a/doc/pub/Bayesian/html/._Bayesian-bs001.html +++ b/doc/pub/Bayesian/html/._Bayesian-bs001.html @@ -41,7 +41,7 @@ Automatically generated HTML file from DocOnce source

  • What is Bayesian Statistics
    • +
  • Why Bayesian Statistics?
  • Inference
  • Statistical Inference
  • Some history
    • @@ -151,19 +151,29 @@ MathJax.Hub.Config({ -

    What is Bayesian Statistics

    +

    Why Bayesian Statistics?

    -Morten's original plan: Reminder about probabilities from the statistics section -

      -
    1. Product rule
      2. -
    2. Binomial distribution
      3. -
    3. Gaussian PDF
      4. -
    4. other PDFs
      5. -
    5. Bayesian regression analysis
      6. -
    +

    +We have already made ourselves familiar with elements of a statistical +data analysis via quantities like the bias-variance tradeoff as well +as some central distribution functions such as the Normal +distribution, the binomial distribution and other probability +distribution functions. + +

    +In essentially all the Machine Learning +algorithms we have studied, our focus has been on a so-called +frequentist approach, where knowledge of an underlying likelihood +function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. + +

    +Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. +We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem. + +

    diff --git a/doc/pub/Bayesian/html/Bayesian-bs.html b/doc/pub/Bayesian/html/Bayesian-bs.html index 426734bac..73bb9265d 100644 --- a/doc/pub/Bayesian/html/Bayesian-bs.html +++ b/doc/pub/Bayesian/html/Bayesian-bs.html @@ -41,7 +41,7 @@ Automatically generated HTML file from DocOnce source
  • What is Bayesian Statistics
    • +
  • Why Bayesian Statistics?
  • Inference
  • Statistical Inference
  • Some history
    • @@ -175,7 +175,7 @@ MathJax.Hub.Config({
    [3] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Jun 7, 2019

    +

    Jun 8, 2019


    diff --git a/doc/pub/Bayesian/html/Bayesian-reveal.html b/doc/pub/Bayesian/html/Bayesian-reveal.html index 1573a0d48..74170c6a2 100644 --- a/doc/pub/Bayesian/html/Bayesian-reveal.html +++ b/doc/pub/Bayesian/html/Bayesian-reveal.html @@ -153,7 +153,7 @@ MathJax.Hub.Config({

    [3] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

     
    -

    Jun 7, 2019

    +

    Jun 8, 2019


    @@ -164,19 +164,27 @@ MathJax.Hub.Config({

    -

    What is Bayesian Statistics

    +

    Why Bayesian Statistics?

    -Morten's original plan: Reminder about probabilities from the statistics section +We have already made ourselves familiar with elements of a statistical +data analysis via quantities like the bias-variance tradeoff as well +as some central distribution functions such as the Normal +distribution, the binomial distribution and other probability +distribution functions. + +

    +In essentially all the Machine Learning +algorithms we have studied, our focus has been on a so-called +frequentist approach, where knowledge of an underlying likelihood +function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. + +

    +Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. +We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem. + -

      -

    1. Product rule
      2. -

    2. Binomial distribution
      3. -

    3. Gaussian PDF
      4. -

    4. other PDFs
      5. -

    5. Bayesian regression analysis
      6. -
    diff --git a/doc/pub/Bayesian/html/Bayesian-solarized.html b/doc/pub/Bayesian/html/Bayesian-solarized.html index 836aea2f3..596cea2b5 100644 --- a/doc/pub/Bayesian/html/Bayesian-solarized.html +++ b/doc/pub/Bayesian/html/Bayesian-solarized.html @@ -61,7 +61,7 @@ div { text-align: justify; text-justify: inter-word; } +

    Jun 8, 2019












    -

    What is Bayesian Statistics

    +

    Why Bayesian Statistics?

    -Morten's original plan: Reminder about probabilities from the statistics section -

      -
    1. Product rule
      2. -
    2. Binomial distribution
      3. -
    3. Gaussian PDF
      4. -
    4. other PDFs
      5. -
    5. Bayesian regression analysis
      6. -
    +

    +We have already made ourselves familiar with elements of a statistical +data analysis via quantities like the bias-variance tradeoff as well +as some central distribution functions such as the Normal +distribution, the binomial distribution and other probability +distribution functions. + +

    +In essentially all the Machine Learning +algorithms we have studied, our focus has been on a so-called +frequentist approach, where knowledge of an underlying likelihood +function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. + +

    +Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. +We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem. + +

    diff --git a/doc/pub/Bayesian/html/Bayesian.html b/doc/pub/Bayesian/html/Bayesian.html index 533aa79b6..4bceafc90 100644 --- a/doc/pub/Bayesian/html/Bayesian.html +++ b/doc/pub/Bayesian/html/Bayesian.html @@ -66,7 +66,7 @@ div { text-align: justify; text-justify: inter-word; } +

    Jun 8, 2019












    -

    What is Bayesian Statistics

    +

    Why Bayesian Statistics?

    -Morten's original plan: Reminder about probabilities from the statistics section -

      -
    1. Product rule
      2. -
    2. Binomial distribution
      3. -
    3. Gaussian PDF
      4. -
    4. other PDFs
      5. -
    5. Bayesian regression analysis
      6. -
    +

    +We have already made ourselves familiar with elements of a statistical +data analysis via quantities like the bias-variance tradeoff as well +as some central distribution functions such as the Normal +distribution, the binomial distribution and other probability +distribution functions. + +

    +In essentially all the Machine Learning +algorithms we have studied, our focus has been on a so-called +frequentist approach, where knowledge of an underlying likelihood +function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. + +

    +Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. +We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem. + +

    diff --git a/doc/pub/Bayesian/ipynb/Bayesian.ipynb b/doc/pub/Bayesian/ipynb/Bayesian.ipynb index 7b7a82bc4..09b2fe4b8 100644 --- a/doc/pub/Bayesian/ipynb/Bayesian.ipynb +++ b/doc/pub/Bayesian/ipynb/Bayesian.ipynb @@ -12,24 +12,28 @@ "\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: **Jun 7, 2019**\n", + "Date: **Jun 8, 2019**\n", "\n", "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", "\n", "\n", "\n", - "## What is Bayesian Statistics\n", - "Morten's original plan: Reminder about probabilities from the statistics section\n", - "1. Product rule\n", + "## Why Bayesian Statistics?\n", "\n", - "2. Binomial distribution\n", + "We have already made ourselves familiar with elements of a statistical\n", + "data analysis via quantities like the bias-variance tradeoff as well\n", + "as some central distribution functions such as the Normal\n", + "distribution, the binomial distribution and other probability\n", + "distribution functions. \n", "\n", - "3. Gaussian PDF\n", + "In essentially all the Machine Learning\n", + "algorithms we have studied, our focus has been on a so-called\n", + "**frequentist approach**, where knowledge of an underlying likelihood\n", + "function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. \n", "\n", - "4. other PDFs\n", - "\n", - "5. Bayesian regression analysis\n", + "Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. \n", + "We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. 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!bblock -Morten's original plan: Reminder about probabilities from the statistics section -o Product rule -o Binomial distribution -o Gaussian PDF -o other PDFs -o Bayesian regression analysis + +We have already made ourselves familiar with elements of a statistical +data analysis via quantities like the bias-variance tradeoff as well +as some central distribution functions such as the Normal +distribution, the binomial distribution and other probability +distribution functions. + +In essentially all the Machine Learning +algorithms we have studied, our focus has been on a so-called +_frequentist approach_, where knowledge of an underlying likelihood +function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure. + +Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. +We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem. + !eblock !split diff --git a/doc/web/course.do.txt b/doc/web/course.do.txt index c4f14d9d1..dc3f15f14 100644 --- a/doc/web/course.do.txt +++ b/doc/web/course.do.txt @@ -18,7 +18,7 @@ chapters = { 'Linalg': 'Review of central linear algebra elements', 'Statistics': 'Monte Carlo methods and elements of probability theory', 'Regression': 'Regression Methods', - 'Splines': 'Gradient methods', + 'Splines': 'Gradient methods and Minimization Algorithms', 'LogReg': 'Logistic Regression', 'NeuralNet': 'Neural Networks', 'DimRed': 'Reduction of dimensionality', @@ -29,7 +29,7 @@ chapters = { 'Autoencoders': 'Autoencoders', 'Reinforce': 'Reinforcement Learning', 'odenn': 'Solving ordinary and partial differential equations with Neural Networks', - 'Bayesian': 'Elements of Bayesian theory', + 'Bayesian': 'Elements of Bayesian theory and Bayesian Neural Networks', 'summary': 'Summary', } %> diff --git a/doc/web/course.html b/doc/web/course.html index 675973cce..50cfe61ab 100644 --- a/doc/web/course.html +++ b/doc/web/course.html @@ -6,6 +6,7 @@ Automatically generated HTML file from DocOnce source + Overview of course material: Data Analysis and Machine Learning @@ -83,7 +84,10 @@ div { text-align: justify; text-justify: inter-word; } None, '___sec4'), ('Regression Methods', 2, None, '___sec5'), - ('Gradient methods', 2, None, '___sec6'), + ('Gradient methods and Minimization Algorithms', + 2, + None, + '___sec6'), ('Logistic Regression', 2, None, '___sec7'), ('Neural Networks', 2, None, '___sec8'), ('Reduction of dimensionality', 2, None, '___sec9'), @@ -104,7 +108,10 @@ div { text-align: justify; text-justify: inter-word; } 2, None, '___sec16'), - ('Elements of Bayesian theory', 2, None, '___sec17'), + ('Elements of Bayesian theory and Bayesian Neural Networks', + 2, + None, + '___sec17'), ('Summary', 2, None, '___sec18'), ('Python and Scikit Learn, a short guide', 2, None, '___sec19'), ('Teach yourself C++', 2, None, '___sec20'), @@ -366,7 +373,7 @@ formulas in HTML or ipython notebook files. -

      Gradient methods

      +

      Gradient methods and Minimization Algorithms

      • LaTeX PDF:
        • @@ -685,7 +692,7 @@ formulas in HTML or ipython notebook files.
      -

      Elements of Bayesian theory

      +

      Elements of Bayesian theory and Bayesian Neural Networks

      • LaTeX PDF: