FIGURE 813 Data with two features and two classes blue and orange displaying a

Figure 813 data with two features and two classes

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•• FIGURE 8.13. Data with two features and two classes (blue and orange), displaying a pure interaction. The left panel shows the partition found by three splits of a standard, greedy, tree-growing algorithm. The ver- tical grey line near the left edge is the first split, and the broken lines are the two subsequent splits. The al- gorithm has no idea where to make a good initial split, and makes a poor choice. The right panel shows the near-optimal splits found by bumping the tree-growing algorithm 20 times.
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Bagging and Bumping Bagging and Random Forests Boosting Methods Boosting Trees Bagging (Revisited) The bagging estimate is defined as ˆ f bag ( x ) = 1 B B X b = 1 ˆ f * b ( x ) for regression and ˆ f bag ( x ) = max k B X b = 1 I { ˆ f * b ( x )= k } for classification where k K are the possible classes. c 2019 The Trustees of the Stevens Institute of Technology
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Bagging and Bumping Bagging and Random Forests Boosting Methods Boosting Trees Out-of-Bag Error 1. Predict response for the i th observation using the trees that did not utilize this observation in their construction 2. Take the average of these responses (or majority vote) to get a single OOB prediction for each of the n observations 3. Use these to calculate the OOB MSE or the OOB Classification error c 2019 The Trustees of the Stevens Institute of Technology
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Bagging and Bumping Bagging and Random Forests Boosting Methods Boosting Trees Random Forests 1. Create a bootstrapped sample of the observations 2. Build a tree, but at each split, only consider m p predictors 3. Use the trees built in this way to calculate your prediction like in bagging.
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