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Morten Hjorth-Jensen
2021-11-20 10:34:53 +01:00
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<a class="navbar-brand" href="week47-bs.html">Week 47: Support Vector Machines</a>
<a class="navbar-brand" href="week47-bs.html">Week 47: Support Vector Machines and Summary of Course</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<!-- navigation toc: --> <li><a href="._week47-bs001.html#___sec0" style="font-size: 80%;">Overview of week 47</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs002.html#___sec1" style="font-size: 80%;">Thursday</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs003.html#___sec2" style="font-size: 80%;">Friday</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs004.html#___sec3" style="font-size: 80%;">Workshop plan Friday (first lecture)</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs005.html#___sec4" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs006.html#___sec5" style="font-size: 80%;">Hyperplanes and all that</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs007.html#___sec6" style="font-size: 80%;">What is a hyperplane?</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs008.html#___sec7" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs009.html#___sec8" style="font-size: 80%;">The two-dimensional case</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs010.html#___sec9" style="font-size: 80%;">Getting into the details</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs011.html#___sec10" style="font-size: 80%;">First attempt at a minimization approach</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs012.html#___sec11" style="font-size: 80%;">Solving the equations</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs013.html#___sec12" style="font-size: 80%;">Can we code this?</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs014.html#___sec13" style="font-size: 80%;">A better approach</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs015.html#___sec14" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs016.html#___sec15" style="font-size: 80%;">Adding the Multiplier</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs017.html#___sec16" style="font-size: 80%;">Setting up the Problem</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs018.html#___sec17" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs019.html#___sec18" style="font-size: 80%;">The last steps</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs020.html#___sec19" style="font-size: 80%;">A soft classifier</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs021.html#___sec20" style="font-size: 80%;">Soft optmization problem</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs001.html#overview-of-week-47" style="font-size: 80%;">Overview of week 47</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs002.html#support-vector-machines-overarching-aims" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs003.html#hyperplanes-and-all-that" style="font-size: 80%;">Hyperplanes and all that</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs004.html#what-is-a-hyperplane" style="font-size: 80%;">What is a hyperplane?</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs005.html#a-p-dimensional-space-of-features" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs006.html#the-two-dimensional-case" style="font-size: 80%;">The two-dimensional case</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs007.html#getting-into-the-details" style="font-size: 80%;">Getting into the details</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs008.html#first-attempt-at-a-minimization-approach" style="font-size: 80%;">First attempt at a minimization approach</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs009.html#solving-the-equations" style="font-size: 80%;">Solving the equations</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs010.html#code-example" style="font-size: 80%;">Code Example</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs011.html#problems-with-the-simpler-approach" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs012.html#a-better-approach" style="font-size: 80%;">A better approach</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs013.html#a-quick-reminder-on-lagrangian-multipliers" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs014.html#adding-the-multiplier" style="font-size: 80%;">Adding the Multiplier</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs015.html#setting-up-the-problem" style="font-size: 80%;">Setting up the Problem</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs017.html#the-last-steps" style="font-size: 80%;">The last steps</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs018.html#a-soft-classifier" style="font-size: 80%;">A soft classifier</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs019.html#soft-optmization-problem" style="font-size: 80%;">Soft optmization problem</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs020.html#kernels-and-non-linearity" style="font-size: 80%;">Kernels and non-linearity</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs021.html#the-equations" style="font-size: 80%;">The equations</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs023.html#different-kernels-and-mercer-s-theorem" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs024.html#the-moons-example" style="font-size: 80%;">The moons example</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs025.html#mathematical-optimization-of-convex-functions" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs028.html#back-to-the-more-realistic-cases" style="font-size: 80%;">Back to the more realistic cases</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs029.html#summary-of-course" style="font-size: 80%;">Summary of course</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs030.html#what-me-worry-no-final-exam-in-this-course" style="font-size: 80%;">What? Me worry? No final exam in this course!</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs031.html#topics-we-have-covered-this-year" style="font-size: 80%;">Topics we have covered this year</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs034.html#learning-outcomes-and-overarching-aims-of-this-course" style="font-size: 80%;">Learning outcomes and overarching aims of this course</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs035.html#perspective-on-machine-learning" style="font-size: 80%;">Perspective on Machine Learning</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs036.html#machine-learning-research" style="font-size: 80%;">Machine Learning Research</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs037.html#starting-your-machine-learning-project" style="font-size: 80%;">Starting your Machine Learning Project</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs038.html#choose-a-model-and-algorithm" style="font-size: 80%;">Choose a Model and Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs039.html#preparing-your-data" style="font-size: 80%;">Preparing Your Data</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs040.html#which-activation-and-weights-to-choose-in-neural-networks" style="font-size: 80%;">Which Activation and Weights to Choose in Neural Networks</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs041.html#optimization-methods-and-hyperparameters" style="font-size: 80%;">Optimization Methods and Hyperparameters</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs042.html#resampling" style="font-size: 80%;">Resampling</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs043.html#other-courses-on-data-science-and-machine-learning-at-uio" style="font-size: 80%;">Other courses on Data science and Machine Learning at UiO</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs044.html#additional-courses-of-interest" style="font-size: 80%;">Additional courses of interest</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs045.html#what-s-the-future-like" style="font-size: 80%;">What's the future like?</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs046.html#types-of-machine-learning-a-repetition" style="font-size: 80%;">Types of Machine Learning, a repetition</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs047.html#why-boltzmann-machines" style="font-size: 80%;">Why Boltzmann machines?</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs048.html#boltzmann-machines" style="font-size: 80%;">Boltzmann Machines</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs049.html#some-similarities-and-differences-from-dnns" style="font-size: 80%;">Some similarities and differences from DNNs</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs050.html#boltzmann-machines-bm" style="font-size: 80%;">Boltzmann machines (BM)</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs051.html#a-standard-bm-setup" style="font-size: 80%;">A standard BM setup</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs052.html#the-structure-of-the-rbm-network" style="font-size: 80%;">The structure of the RBM network</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs053.html#the-network" style="font-size: 80%;">The network</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs054.html#goals" style="font-size: 80%;">Goals</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs055.html#joint-distribution" style="font-size: 80%;">Joint distribution</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs056.html#network-elements-the-energy-function" style="font-size: 80%;">Network Elements, the energy function</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs057.html#defining-different-types-of-rbms" style="font-size: 80%;">Defining different types of RBMs</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs058.html#more-about-rbms" style="font-size: 80%;">More about RBMs</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs059.html#autoencoders-overarching-view" style="font-size: 80%;">Autoencoders: Overarching view</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs060.html#bayesian-machine-learning" style="font-size: 80%;">Bayesian Machine Learning</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs061.html#reinforcement-learning" style="font-size: 80%;">Reinforcement Learning</a></li>
<!-- navigation toc: --> <li><a href="._week47-bs062.html#transfer-learning" style="font-size: 80%;">Transfer learning</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs067.html#the-challenges-facing-machine-learning" style="font-size: 80%;">The Challenges Facing Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs074.html#the-last-words" style="font-size: 80%;">The last words?</a></li>
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<center><h1>Week 47: Support Vector Machines</h1></center> <!-- document title -->
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<h1>Week 47: Support Vector Machines and Summary of Course</h1>
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<!-- author(s): Morten Hjorth-Jensen -->
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<!-- institution(s) -->
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[1] <b>Department of Physics, University of Oslo</b>
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[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b>
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<h4>Nov 20, 2021</h4>
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<center><h4>Nov 26, 2020</h4></center> <!-- date -->
<br>
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<p><a href="._week47-bs001.html" class="btn btn-primary btn-lg">Read &raquo;</a></p>
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<li><a href="._week47-bs075.html">76</a></li>
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<!-- copyright --> &copy; 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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