Morten Hjorth-Jensen
396 lines
23 KiB
HTML
396 lines
23 KiB
HTML
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<a class="navbar-brand" href="week44-bs.html">Week 44: Dimensionality Reduction, PCA and Clustering. Decision Trees</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="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs004.html#learning-rate-and-more" style="font-size: 80%;">Learning Rate and more</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs005.html#thursday-principal-component-analysis" style="font-size: 80%;">Thursday, Principal Component Analysis</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-kind-of-bird-s-view-on-pca" style="font-size: 80%;">A kind of Bird's view on PCA</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs007.html#thursday-clustering-and-unsupervised-learning" style="font-size: 80%;">Thursday: Clustering and Unsupervised Learning</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs008.html#basic-idea-of-the-k-means-clustering-algorithm" style="font-size: 80%;">Basic Idea of the \( k \)-means Clustering Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs009.html#the-k-means-algorithm" style="font-size: 80%;">The \( k \)-means Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs010.html#basic-math-of-the-k-means-algorithm" style="font-size: 80%;">Basic Math of the \( k \)-means Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs011.html#within-cluster-point-scatter" style="font-size: 80%;">Within Cluster Point Scatter</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs012.html#more-details" style="font-size: 80%;">More Details</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs013.html#total-cluster-variance" style="font-size: 80%;">Total Cluster Variance</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs014.html#the-k-means-clustering-algorithm" style="font-size: 80%;">The \( k \)-means Clustering Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs015.html#summarizing" style="font-size: 80%;">Summarizing</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs016.html#writing-our-own-code-the-data-set" style="font-size: 80%;">Writing our own Code, the Data Set</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs017.html#implementing-the-k-means-algorithm" style="font-size: 80%;">Implementing the \( k \)-means Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs018.html#plotting" style="font-size: 80%;">Plotting</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs019.html#continuing" style="font-size: 80%;">Continuing</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs020.html#wrapping-it-up" style="font-size: 80%;">Wrapping it up</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs021.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs022.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs023.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs024.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs025.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>
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<!-- navigation toc: --> <li><a href="._week44-bs026.html#general-features" style="font-size: 80%;">General Features</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs027.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs028.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs029.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs030.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="._week44-bs031.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs032.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs033.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs034.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs035.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs036.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs037.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="._week44-bs038.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs039.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="._week44-bs040.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="._week44-bs041.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs042.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="._week44-bs043.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="._week44-bs044.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="._week44-bs045.html#computing-the-gini-index" style="font-size: 80%;">Computing the Gini index</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs046.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="._week44-bs047.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs048.html#entropy-and-the-id3-algorithm" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs049.html#cancer-data-again-now-with-decision-trees-and-other-methods" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs050.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs051.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs052.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs053.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs054.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="._week44-bs055.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs056.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="._week44-bs057.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="._week44-bs058.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="._week44-bs060.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="._week44-bs061.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs062.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs063.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs064.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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<a name="part0059"></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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