The fast convergence of boosting

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This manuscript considers the convergence rate of boosting under a large class of losses, including the exponential and logistic losses, where the best previous rate of convergence was O(exp(1/ε 2)). First, it is established that the setting of weak learnability aids the entire class, granting a rate O(ln(1/ε)). Next, the (disjoint) conditions under which the infimal empirical risk is attainable are characterized in terms of the sample and weak learning class, and a new proof is given for the known rate O(ln(1/ε)). Finally, it is established that any instance can be decomposed into two smaller instances resembling the two preceding special cases, yielding a rate O(1/ε), with a matching lower bound for the logistic loss. The principal technical hurdle throughout this work is the potential unattainability of the infimal empirical risk; the technique for overcoming this barrier may be of general interest.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 24
Subtitle of host publication25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
StatePublished - Dec 1 2011
Externally publishedYes
Event25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011 - Granada, Spain
Duration: Dec 12 2011Dec 14 2011

Publication series

NameAdvances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Other

Other25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
CountrySpain
CityGranada
Period12/12/1112/14/11

ASJC Scopus subject areas

  • Information Systems

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