Morten Hjorth-Jensen
350 lines
20 KiB
HTML
350 lines
20 KiB
HTML
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<a class="navbar-brand" href="week39-bs.html">Week 39: Optimization and Gradient Methods</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week39-bs001.html#plan-for-week-39" style="font-size: 80%;">Plan for week 39</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs002.html#thursday-september-29" style="font-size: 80%;">Thursday September 29</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs003.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;">Searching for Optimal Regularization Parameters \( \lambda \)</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs004.html#grid-search" style="font-size: 80%;">Grid Search</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs005.html#randomized-grid-search" style="font-size: 80%;">Randomized Grid Search</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs006.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs007.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs008.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs009.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs010.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs011.html#the-equations" style="font-size: 80%;">The equations</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs012.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs013.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs014.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs015.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs016.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs017.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs018.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs019.html#convex-function" style="font-size: 80%;">Convex function</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs020.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs021.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs022.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs023.html#standard-steepest-descent" style="font-size: 80%;">Standard steepest descent</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs024.html#gradient-method" style="font-size: 80%;">Gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs026.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs026.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs027.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs028.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs033.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs036.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs037.html#revisiting-our-first-homework" style="font-size: 80%;">Revisiting our first homework</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs042.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs039.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs040.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs041.html#simple-program" style="font-size: 80%;">Simple program</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs042.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs043.html#and-a-corresponding-example-using-scikit-learn" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs044.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs045.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs046.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs047.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs048.html#challenge-yourself" style="font-size: 80%;">Challenge yourself</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs049.html#friday-september-30" style="font-size: 80%;">Friday September 30</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs050.html#stochastic-gradient-descent" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs051.html#computation-of-gradients" style="font-size: 80%;">Computation of gradients</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs052.html#sgd-example" style="font-size: 80%;">SGD example</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs053.html#the-gradient-step" style="font-size: 80%;">The gradient step</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs054.html#simple-example-code" style="font-size: 80%;">Simple example code</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs055.html#when-do-we-stop" style="font-size: 80%;">When do we stop?</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs056.html#slightly-different-approach" style="font-size: 80%;">Slightly different approach</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs057.html#program-for-stochastic-gradient" style="font-size: 80%;">Program for stochastic gradient</a></li>
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<!-- navigation toc: --> <li><a href="._week39-bs058.html#code-with-a-number-of-minibatches-which-varies" style="font-size: 80%;">Code with a Number of Minibatches which varies</a></li>
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</ul>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0000"></a>
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<!-- ------------------- main content ---------------------- -->
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<div class="jumbotron">
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<center>
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<h1>Week 39: Optimization and Gradient Methods</h1>
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</center> <!-- document title -->
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<!-- institution(s) -->
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<center>
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[1] <b>Department of Physics, University of Oslo</b>
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</center>
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<center>
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[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b>
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</center>
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<br>
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<center>
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<h4>Aug 23, 2022</h4>
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</center> <!-- date -->
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<br>
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<p><a href="._week39-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
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<li class="active"><a href="._week39-bs000.html">1</a></li>
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<li><a href="._week39-bs001.html">2</a></li>
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<li><a href="._week39-bs002.html">3</a></li>
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<li><a href="._week39-bs003.html">4</a></li>
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<li><a href="._week39-bs004.html">5</a></li>
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<li><a href="._week39-bs005.html">6</a></li>
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<li><a href="._week39-bs006.html">7</a></li>
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<li><a href="._week39-bs007.html">8</a></li>
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<li><a href="._week39-bs008.html">9</a></li>
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<li><a href="._week39-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week39-bs058.html">59</a></li>
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<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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<!-- Bootstrap footer
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<footer>
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<a href="https://..."><img width="250" align=right src="https://..."></a>
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</footer>
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-->
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</body>
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</html>
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