A Brief Introduction to Adaboost

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1 A Brief Introduction to Adaboost Hongbo Deng 6 Feb, 2007 Some of the slides are borrowed from Derek Hoiem & Jan ˇSochman. 1

2 Outline Background Adaboost Algorithm Theory/Interpretations 2

3 What s So Good About Adaboost Can be used with many different classifiers Improves classification accuracy Commonly used in many areas Simple to implement Not prone to overfitting 3

4 A Brief History Resampling for estimating statistic Bootstrapping Bagging Boosting (Schapire 1989) Resampling for classifier design Adaboost (Schapire 1995) 4

5 Bootstrap Estimation Repeatedly draw n samples from D For each set of samples, estimate a statistic The bootstrap estimate is the mean of the individual estimates Used to estimate a statistic (parameter) and its variance 5

6 Bagging - Aggregate Bootstrapping For i = 1.. M Draw n * <n samples from D with replacement Learn classifier C i Final classifier is a vote of C 1.. C M Increases classifier stability/reduces variance D1 D2 D3 D 6

7 Boosting (Schapire 1989) Consider creating three component classifiers for a two-category problem through boosting. Randomly select n 1 < n samples from D without replacement to obtain D 1 Train weak learner C 1 Select n 2 < n samples from D with half of the samples misclassified by C 1 to obtain D 2 Train weak learner C 2 Select all remaining samples from D that C 1 and C 2 disagree on Train weak learner C 3 Final classifier is vote of weak learners D1 D3 D D

8 Adaboost - Adaptive Boosting Instead of resampling, uses training set re-weighting Each training sample uses a weight to determine the probability of being selected for a training set. AdaBoost is an algorithm for constructing a strong classifier as linear combination of simple weak classifier Final classification based on weighted vote of weak classifiers 8

9 Adaboost Terminology h t (x) weak or basis classifier (Classifier = Learner = Hypothesis) strong or final classifier Weak Classifier: < 50% error over any distribution Strong Classifier: thresholded linear combination of weak classifier outputs 9

10 Discrete Adaboost Algorithm Each training sample has a weight, which determines the probability of being selected for training the component classifier 10

11 Find the Weak Classifier 11

12 Find the Weak Classifier 12

13 The algorithm core 13

14 Reweighting y * h(x) = 1 y * h(x) = -1 14

15 Reweighting In this way, AdaBoost focused on the informative or difficult examples. 15

16 Reweighting In this way, AdaBoost focused on the informative or difficult examples. 16

17 Algorithm recapitulation t = 1 17

18 Algorithm recapitulation 18

19 Algorithm recapitulation 19

20 Algorithm recapitulation 20

21 Algorithm recapitulation 21

22 Algorithm recapitulation 22

23 Algorithm recapitulation 23

24 Algorithm recapitulation 24

25 Pros and cons of AdaBoost Advantages Very simple to implement Does feature selection resulting in relatively simple classifier Fairly good generalization Disadvantages Suboptimal solution Sensitive to noisy data and outliers 25

26 References Duda, Hart, ect Pattern Classification Freund An adaptive version of the boost by majority algorithm Freund Experiments with a new boosting algorithm Freund, Schapire A decision-theoretic generalization of on-line learning and an application to boosting Friedman, Hastie, etc Additive Logistic Regression: A Statistical View of Boosting Jin, Liu, etc (CMU) A New Boosting Algorithm Using Input-Dependent Regularizer Li, Zhang, etc Floatboost Learning for Classification Opitz, Maclin Popular Ensemble Methods: An Empirical Study Ratsch, Warmuth Efficient Margin Maximization with Boosting Schapire, Freund, etc Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods Schapire, Singer Improved Boosting Algorithms Using Confidence-Weighted Predictions Schapire The Boosting Approach to Machine Learning: An overview Zhang, Li, etc Multi-view Face Detection with Floatboost 26

27 Appendix Bound on training error Adaboost Variants 27

28 Bound on Training Error (Schapire) 28

29 Discrete Adaboost (DiscreteAB) (Friedman s wording) 29

30 Discrete Adaboost (DiscreteAB) (Freund and Schapire s wording) 30

31 Adaboost with Confidence Weighted Predictions (RealAB) 31

32 Adaboost Variants Proposed By Friedman LogitBoost Solves Requires care to avoid numerical problems GentleBoost Update is f m (x) = P(y=1 x) P(y=0 x) instead of Bounded [0 1] 32

33 Adaboost Variants Proposed By Friedman LogitBoost 33

34 Adaboost Variants Proposed By Friedman GentleBoost 34

35 Thanks!!! Any comments or questions? 35

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