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Unformatted text preview: Bagging and Boosting: Brief Introduction Bagging and Boosting: Brief Introduction Jia Li Department of Statistics The Pennsylvania State University Email: jiali@stat.psu.edu http://www.stat.psu.edu/jiali Jia Li http://www.stat.psu.edu/jiali Bagging and Boosting: Brief Introduction Overview Bagging and boosting are meta-algorithms that pool decisions from multiple classifiers. Much information can be found on Wikipedia. Jia Li http://www.stat.psu.edu/jiali Bagging and Boosting: Brief Introduction Overview on Bagging Invented by Leo Breiman: Bootstrap aggregating. L. Breiman, "Bagging predictors," Machine Learning, 24(2):123-140, 1996. Majority vote from classifiers trained on bootstrap samples of the training data. Jia Li http://www.stat.psu.edu/jiali Bagging and Boosting: Brief Introduction Bagging Generate B bootstrap samples of the training data: random sampling with replacement. Train a classifier or a regression function using each bootstrap sample. For classification: majority vote on the classification results. For regression: average on the predicted values. Reduces variation. Improves performance for unstable classifiers which vary significantly with small changes in the data set, e.g., CART. Found to improve CART a lot, but not the nearest neighbor classifier. http://www.stat.psu.edu/jiali Jia Li Bagging and Boosting: Brief Introduction Overview on Boosting Iteratively learning weak classifiers Final result is the weighted sum of the results of weak classifiers. Many different kinds of boosting algorithms: Adaboost (Adaptive boosting) by Y. Freund and R. Schapire is the first. Examples of other boosting algorithms: LPBoost: Linear Programming Boosting is a margin-maximizing classification algorithm with boosting. BrownBoost: increase robustness against noisy datasets. Discard points that are repeatedly misclassified. LogitBoost: J. Friedman, T. Hastie and R. Tibshirani, "Additive logistic regression: a statistical view of boosting," Annals of Statistics, 28(2), 337-407, 2000. Jia Li http://www.stat.psu.edu/jiali Bagging and Boosting: Brief Introduction Adaboost for Binary Classification 1. Training data: (xi , yi ), i = 1, ..., n, xi X , yi Y = {-1, 1}. 1 2. Let w1,i = n , i = 1, ..., n. 3. For t = 1, ..., T : 3.1 Learn classifier ht : X Y from a set of weak classifiers called hypotheses, H = {h(, )| }, that minimizes the error rate with respect to distribution wt,i over xi 's. n 3.2 Let rt = i=1 wt,i I (yi = ht (xi )). If rt > 0.5, stop. 3.3 Choose t R. Usually set t = 1 log 1-rt . 2 rt 3.4 Update wt+1,i =t,i Zt , where Zt is a normalization factor to ensure i wt+1,i = 1. w e -t yi ht (xi ) 4. Output the final classifier: f (x) = sign Note: the update of wt,i implies incorrectly classified points receive increased weights in the next round of learning. Jia Li http://www.stat.psu.edu/jiali T t=1 t ht (x) . ...
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This note was uploaded on 02/04/2012 for the course STAT 557 taught by Professor Jiali during the Fall '09 term at Pennsylvania State University, University Park.

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