mhjensen
273 lines
14 KiB
HTML
273 lines
14 KiB
HTML
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<a class="navbar-brand" href="week44-bs.html">week 44: From Decision Trees to Bagging 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="._week44-bs001.html#___sec0" style="font-size: 80%;">Decision trees, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs002.html#___sec1" 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-bs003.html#___sec2" style="font-size: 80%;">General Features</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs004.html#___sec3" style="font-size: 80%;">How do we set it up?</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs005.html#___sec4" style="font-size: 80%;">Decision trees and Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs006.html#___sec5" style="font-size: 80%;">Building a tree, regression</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs007.html#___sec6" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs008.html#___sec7" style="font-size: 80%;">Making a tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs009.html#___sec8" style="font-size: 80%;">Pruning the tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs010.html#___sec9" style="font-size: 80%;">Cost complexity pruning</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs011.html#___sec10" style="font-size: 80%;">Schematic Regression Procedure</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs012.html#___sec11" style="font-size: 80%;">A Classification Tree</a></li>
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<!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;">Growing a classification tree</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs014.html#___sec13" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs015.html#___sec14" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs016.html#___sec15" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs017.html#___sec16" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs018.html#___sec17" style="font-size: 80%;">The CART algorithm for Classification</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs019.html#___sec18" style="font-size: 80%;">The CART algorithm for Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs020.html#___sec19" style="font-size: 80%;">Computing the Gini index</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs021.html#___sec20" 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-bs022.html#___sec21" style="font-size: 80%;">Computing the Gini Factor</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs023.html#___sec22" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs024.html#___sec23" style="font-size: 80%;">Implementing the ID3 Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs025.html#___sec24" 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-bs026.html#___sec25" style="font-size: 80%;">Another example, the moons again</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs027.html#___sec26" style="font-size: 80%;">Playing around with regions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs028.html#___sec27" style="font-size: 80%;">Regression trees</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs029.html#___sec28" style="font-size: 80%;">Final regressor code</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs030.html#___sec29" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs031.html#___sec30" style="font-size: 80%;">Disadvantages</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs032.html#___sec31" 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-bs033.html#___sec32" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs034.html#___sec33" style="font-size: 80%;">Bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs035.html#___sec34" style="font-size: 80%;">More bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs036.html#___sec35" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs037.html#___sec36" style="font-size: 80%;">Using the Voting Classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs038.html#___sec37" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs039.html#___sec38" style="font-size: 80%;">Bagging Examples</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs040.html#___sec39" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0013"></a>
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<!-- !split -->
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<h2 id="___sec12" class="anchor">Growing a classification tree </h2>
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<p>
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The task of growing a
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classification tree is quite similar to the task of growing a
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regression tree. Just as in the regression setting, we use recursive
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binary splitting to grow a classification tree. However, in the
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classification setting, the MSE cannot be used as a criterion for making
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the binary splits. A natural alternative to MSE is the <b>classification
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error rate</b>. Since we plan to assign an observation in a given region
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to the most commonly occurring error rate class of training
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observations in that region, the classification error rate is simply
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the fraction of the training observations in that region that do not
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belong to the most common class.
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<p>
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When building a classification tree, either the Gini index or the
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entropy are typically used to evaluate the quality of a particular
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split, since these two approaches are more sensitive to node purity
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than is the classification error rate.
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<p>
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<p>
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