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Boosting1

Boosting1 - ICML 2009 Tutorial Survey of Boosting from an...

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ICML 2009 Tutorial Survey of Boosting from an Optimization Perspective Part I: Entropy Regularized LPBoost Part II: Boosting from an Optimization Perspective Manfred K. Warmuth - UCSC S.V.N. Vishwanathan - Purdue & Microsoft Research Updated: March 23, 2010 Warmuth (UCSC) ICML ’09 Boosting Tutorial 1 / 62

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Outline 1 Introduction to Boosting 2 What is Boosting? 3 Entropy Regularized LPBoost 4 Overview of Boosting algorithms 5 Conclusion and Open Problems Warmuth (UCSC) ICML ’09 Boosting Tutorial 2 / 62
Introduction to Boosting Outline 1 Introduction to Boosting 2 What is Boosting? 3 Entropy Regularized LPBoost 4 Overview of Boosting algorithms 5 Conclusion and Open Problems Warmuth (UCSC) ICML ’09 Boosting Tutorial 3 / 62

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Introduction to Boosting Setup for Boosting [Giants of field: Schapire,Freund] examples: 11 apples +1 if artificial - 1 if natural goal: classification Warmuth (UCSC) ICML ’09 Boosting Tutorial 4 / 62
Introduction to Boosting Setup for Boosting +1 / -1 examples weight d n size separable Warmuth (UCSC) ICML ’09 Boosting Tutorial 5 / 62

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Introduction to Boosting Weak hypotheses weak hypotheses: decision stumps on two features one can’t do it goal: find convex combination of weak hypotheses that classifies all Warmuth (UCSC) ICML ’09 Boosting Tutorial 6 / 62
Introduction to Boosting Boosting: 1st iteration First hypothesis: error: 1 11 edge: 9 11 low error = high edge edge = 1 - 2 error Warmuth (UCSC) ICML ’09 Boosting Tutorial 7 / 62

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Introduction to Boosting Update after 1st Misclassified examples increased weights After update edge of hypothesis decreased Warmuth (UCSC) ICML ’09 Boosting Tutorial 8 / 62
Introduction to Boosting Before 2nd iteration Hard examples high weight Warmuth (UCSC) ICML ’09 Boosting Tutorial 9 / 62

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Introduction to Boosting Boosting: 2nd hypothesis Pick hypotheses with high (weighted) edge Warmuth (UCSC) ICML ’09 Boosting Tutorial 10 / 62
Introduction to Boosting Update after 2nd After update edges of all past hypotheses should be small Warmuth (UCSC) ICML ’09 Boosting Tutorial 11 / 62

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Introduction to Boosting 3rd hypothesis Warmuth (UCSC) ICML ’09 Boosting Tutorial 12 / 62
Introduction to Boosting Update after 3rd Warmuth (UCSC) ICML ’09 Boosting Tutorial 13 / 62

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Introduction to Boosting 4th hypothesis Warmuth (UCSC) ICML ’09 Boosting Tutorial 14 / 62
Introduction to Boosting Update after 4th Warmuth (UCSC) ICML ’09 Boosting Tutorial 15 / 62

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Introduction to Boosting Final convex combination of all hypotheses Decision: T t =1 w t h t ( x ) 0 ? Positive total weight - Negative total weight Warmuth (UCSC) ICML ’09 Boosting Tutorial 16 / 62
Introduction to Boosting Protocol of Boosting [FS97] Maintain distribution on N ± 1 labeled examples At iteration t = 1 , . . . , T : - Receive “weak” hypothesis h t of high edge - Update d t - 1 to d t more weights on “hard” examples Output convex combination of the weak hypotheses T t =1 w t h t ( x ) Two sets of weights: - distribution d on examples - distribution w on hypotheses Warmuth (UCSC) ICML ’09 Boosting Tutorial 17 / 62

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Introduction to Boosting Data representation y n h t ( x n ) := u t n perfect +1 opposite -1
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Boosting1 - ICML 2009 Tutorial Survey of Boosting from an...

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