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1. Stat 231. A.L. Yuille. Fall 2004
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  1. 1. Stat 231. A.L. Yuille. Fall 2004 • AdaBoost.. • Summary and Extensions. • Read Viola and Jones Handout. Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  2. 2. Basic AdaBoost Review • Data • Set of weak classifiers • Weights • Parameters • Strong Classifier: Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  3. 3. Basic AdaBoost Algorithm • Initialize • Update Rule: where Z is the normalization constant. • Let • Pick classifier to minimize • Set • Repeat. Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  4. 4. Basic AdaBoost Algorithm • .Errors: • Bounded by, which equals • AdaBoost is a greedy algorithm that tries to minimize the bound by minimizing the Z’s in order w.r.t. Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  5. 5. AdaBoost Variant 1. • In preparation for Viola and Jones. New parameter • Strong classifier • Modify update rule: • Let be the sum of weights if weak class is p, true class q. • Pick weak classifier to minimize set Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  6. 6. AdaBoost Variant 1. • As before: the error is bounded by • Same “trick” If weak classifier is right then: If weak classifier is wrong then: Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  7. 7. AdaBoost Variant 2. • We have assumed a loss function which pays equal penalties for false positives and false negatives. • But we may want false negatives to cost more (Viola and Jones). • Use loss function: Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  8. 8. AdaBoost Variant 2. • Modify the update rule: • Verify that the loss: • Same update rule as for Variant 1, except Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  9. 9. AdaBoost Extensions • AdaBoost can be extended to multiclasses: (Singer and Schapire) • The weak classifiers can have take multiple values. • The conditional probability interpretation applies to these extensions. Lecture notes for Stat 231: Pattern Recognition and Machine Learning

  10. 10. AdaBoost Summary • Basic AdaBoost:. Combine weak classifiers to make a strong classifier. • Dynamically weight the data, so that misclassified data weighs more (like SVM pay more attention to hard-to-classify data). • Exponential convergence to empirical risk (weak conditions). • Useful for combining weak cues for Visual Detection tasks. • Probabilistic Interpretation/Multiclass/Multivalued classifiers. Lecture notes for Stat 231: Pattern Recognition and Machine Learning