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Morten Hjorth-Jensen
2023-11-12 18:58:36 +01:00
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@@ -8,8 +8,8 @@ doconce format html week46.do.txt --html_style=bootstrap --pygments_html_style=d
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<title>Week 46: Support Vector Machines and Project 3.</title>
<meta name="description" content="Week 46: Decision Trees, Ensemble methods and Random Forests">
<title>Week 46: Decision Trees, Ensemble methods and Random Forests</title>
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@@ -125,42 +247,77 @@ MathJax.Hub.Config({
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines and Project 3.</a>
<a class="navbar-brand" href="week46-bs.html">Week 46: Decision Trees, Ensemble methods and Random Forests</a>
</div>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._week46-bs001.html#overview-of-week-46" style="font-size: 80%;">Overview of week 46</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs002.html#support-vector-machines-overarching-aims" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs003.html#hyperplanes-and-all-that" style="font-size: 80%;">Hyperplanes and all that</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#what-is-a-hyperplane" style="font-size: 80%;">What is a hyperplane?</a></li>
<!-- navigation toc: --> <li><a href="._week46-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="._week46-bs006.html#the-two-dimensional-case" style="font-size: 80%;">The two-dimensional case</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#getting-into-the-details" style="font-size: 80%;">Getting into the details</a></li>
<!-- navigation toc: --> <li><a href="._week46-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="._week46-bs009.html#solving-the-equations" style="font-size: 80%;">Solving the equations</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#code-example" style="font-size: 80%;">Code Example</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#problems-with-the-simpler-approach" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#a-better-approach" style="font-size: 80%;">A better approach</a></li>
<!-- navigation toc: --> <li><a href="._week46-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="._week46-bs014.html#adding-the-multiplier" style="font-size: 80%;">Adding the Multiplier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#setting-up-the-problem" style="font-size: 80%;">Setting up the Problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#the-last-steps" style="font-size: 80%;">The last steps</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#a-soft-classifier" style="font-size: 80%;">A soft classifier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#soft-optmization-problem" style="font-size: 80%;">Soft optmization problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#kernels-and-non-linearity" style="font-size: 80%;">Kernels and non-linearity</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#the-equations" style="font-size: 80%;">The equations</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week46-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="._week46-bs024.html#the-moons-example" style="font-size: 80%;">The moons example</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#mathematical-optimization-of-convex-functions" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#how-do-we-solve-these-problems" style="font-size: 80%;">How do we solve these problems?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#a-simple-example" style="font-size: 80%;">A simple example</a></li>
<!-- navigation toc: --> <li><a href="._week46-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="._week46-bs029.html#support-vector-machines-for-regression" style="font-size: 80%;">Support vector machines for regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs001.html#plan-for-week-46" style="font-size: 80%;">Plan for week 46</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs002.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs003.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs005.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs006.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#general-features" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs008.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs009.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs013.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs014.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs016.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs023.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs024.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs028.html#the-table" style="font-size: 80%;">The Table</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs029.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs030.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs031.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs032.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs033.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs034.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs035.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs036.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs037.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs038.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs039.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs040.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs041.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs042.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs043.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs044.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs045.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs046.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs047.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs048.html#bagging" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs049.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs050.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs051.html#random-forests" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs052.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs053.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs054.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs055.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs057.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs058.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs059.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
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<h1>Week 46: Support Vector Machines and Project 3. </h1>
<h1>Week 46: Decision Trees, Ensemble methods and Random Forests</h1>
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<h4>Nov 19, 2022</h4>
<h4>Week 46, November 13-17</h4>
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