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

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Unformatted text preview: 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 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 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 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 +1 /-1 examples weight d n size separable Warmuth (UCSC) ICML 09 Boosting Tutorial 5 / 62 Introduction to Boosting Weak hypotheses 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 weak hypotheses: decision stumps on two features one cant 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 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 First hypothesis: error: 1 11 edge: 9 11 low error = high edge edge = 1- 2 error Warmuth (UCSC) ICML 09 Boosting Tutorial 7 / 62 Introduction to Boosting Update after 1st 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 Misclassified examples increased weights After update edge of hypothesis decreased Warmuth (UCSC) ICML 09 Boosting Tutorial 8 / 62 Introduction to Boosting Before 2nd iteration 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 Hard examples high weight Warmuth (UCSC) ICML 09 Boosting Tutorial 9 / 62 Introduction to Boosting Boosting: 2nd hypothesis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 Pick hypotheses with high (weighted) edge Warmuth (UCSC) ICML 09 Boosting Tutorial 10 / 62 Introduction to Boosting Update after 2nd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 After update edges of all past hypotheses should be small Warmuth (UCSC) ICML 09 Boosting Tutorial 11 / 62 Introduction to Boosting 3rd hypothesis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 Warmuth (UCSC) ICML 09 Boosting Tutorial 12 / 62 Introduction to Boosting Update after 3rd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 feature 1 0.0 0.2 0.4 0.6 0.8 feature 2 Warmuth (UCSC) ICML 09 Boosting Tutorial 13 / 62 Introduction to Boosting...
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This note was uploaded on 02/23/2012 for the course STAT 598 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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

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