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Boosting Rong Jin

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**Inefficiency with Bagging**

D Bagging … D1 D2 Dk Boostrap Sampling h1 h2 hk Inefficient boostrap sampling: Every example has equal chance to be sampled No distinction between “easy” examples and “difficult” examples Inefficient model combination: A constant weight for each classifier No distinction between accurate classifiers and inaccurate classifiers

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**Improve the Efficiency of Bagging**

Better sampling strategy Focus on the examples that are difficult to classify Better combination strategy Accurate model should be assigned larger weights

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**Intuition + + May overfitting !! Mistakes Classifier3 Classifier2**

No training mistakes !! May overfitting !! + Mistakes X1 Y1 + Mistakes X1 Y1 X3 Y3 Training Examples X1 Y1 X2 Y2 X3 Y3 X4 Y4 Pop up note: no mistakes but possible overfitting on training data Road map before boosting Clearify the old works and the proposed methods Less words !!!

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AdaBoost Algorithm

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**AdaBoost Example: t=ln2**

x1, y1 x2, y2 x3, y3 x4, y4 x5, y5 1/5 D0: x5, y5 x3, y3 x1, y1 Sample h1 Training x1, y1 x2, y2 x3, y3 x4, y4 x5, y5 Update Weights h1 Sample x3, y3 x1, y1 2/7 1/7 D1: h2 Training x1, y1 x2, y2 x3, y3 x4, y4 x5, y5 h2 Update Weights 2/9 1/9 4/9 D2: Sample …

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**How To Choose t in AdaBoost?**

How to construct the best distribution Dt+1(i) Dt+1(i) should be significantly different from Dt(i) Dt+1(i) should create a situation that classifier ht performs poorly

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**How To Choose t in AdaBoost?**

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**Optimization View for Choosing t**

ht(x): x{1,-1}; a base (weak) classifier HT(x): a linear combination of basic classifiers Goal: minimize training error Approximate error swith a exponential function

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**AdaBoost: Greedy Optimization**

Fix HT-1(x), and solve hT(x) and t

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**Empirical Study of AdaBoost**

AdaBoosting decision trees Generate 50 decision trees by AdaBoost Linearly combine decision trees using the weights of AdaBoost In general: AdaBoost = Bagging > C4.5 AdaBoost usually needs less number of classifiers than Bagging

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**Bia-Variance Tradeoff for AdaBoost**

AdaBoost can reduce both variance and bias simultaneously variance bias single decision tree Bagging decision tree AdaBoosting decision trees

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