Morten Hjorth-Jensen
410 lines
24 KiB
HTML
410 lines
24 KiB
HTML
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<a class="navbar-brand" href="week47-bs.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting 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="._week47-bs001.html#plan-for-week-47" style="font-size: 80%;">Plan for week 47</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs002.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs003.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs004.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs005.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs006.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs007.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs008.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs009.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs010.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs011.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs012.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs013.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs014.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs015.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs016.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs017.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs018.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs019.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs020.html#the-table" style="font-size: 80%;">The Table</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs021.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs022.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs023.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs024.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>
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<!-- navigation toc: --> <li><a href="._week47-bs025.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs026.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs027.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs028.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs029.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs030.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>
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<!-- navigation toc: --> <li><a href="._week47-bs031.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs032.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs033.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs034.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs035.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs036.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs037.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs038.html#bagging" style="font-size: 80%;">Bagging</a></li>
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<!-- navigation toc: --> <li><a href="#more-bagging" style="font-size: 80%;">More bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs040.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>
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<!-- navigation toc: --> <li><a href="._week47-bs041.html#random-forests" style="font-size: 80%;">Random forests</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs042.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs043.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>
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<!-- navigation toc: --> <li><a href="._week47-bs044.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs045.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs046.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs047.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs048.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs049.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs050.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs051.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs052.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs053.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs054.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs055.html#making-an-adaboost-code-yourself" style="font-size: 80%;">Making an ADAboost code yourself</a></li>
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|
<!-- navigation toc: --> <li><a href="._week47-bs056.html#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent" style="font-size: 80%;">Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs057.html#the-squared-error-again-steepest-descent" style="font-size: 80%;">The Squared-Error again! Steepest Descent</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs058.html#steepest-descent-example" style="font-size: 80%;">Steepest Descent Example</a></li>
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<!-- navigation toc: --> <li><a href="._week47-bs059.html#gradient-boosting-algorithm" style="font-size: 80%;">Gradient Boosting, algorithm</a></li>
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<a name="part0039"></a>
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<!-- !split -->
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<h2 id="more-bagging" class="anchor">More bagging </h2>
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<p>Bagging typically results in improved accuracy
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over prediction using a single tree. Unfortunately, however, it can be
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difficult to interpret the resulting model. Recall that one of the
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advantages of decision trees is the attractive and easily interpreted
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diagram that results.
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</p>
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<p>However, when we bag a large number of trees, it is no longer
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possible to represent the resulting statistical learning procedure
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using a single tree, and it is no longer clear which variables are
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most important to the procedure. Thus, bagging improves prediction
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accuracy at the expense of interpretability. Although the collection
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of bagged trees is much more difficult to interpret than a single
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tree, one can obtain an overall summary of the importance of each
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predictor using the MSE (for bagging regression trees) or the Gini
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index (for bagging classification trees). In the case of bagging
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regression trees, we can record the total amount that the MSE is
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decreased due to splits over a given predictor, averaged over all \( B \) possible
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trees. A large value indicates an important predictor. Similarly, in
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the context of bagging classification trees, we can add up the total
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amount that the Gini index is decreased by splits over a given
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predictor, averaged over all \( B \) trees.
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