Learning bounds for importance weighting

Corinna Cortes, Yishay Mansour, Mehryar Mohri

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

Abstract

This paper presents an analysis of importance weighting for learning from finite samples and gives a series of theoretical and algorithmic results. We point out simple cases where importance weighting can fail, which suggests the need for an analysis of the properties of this technique. We then give both upper and lower bounds for generalization with bounded importance weights and, more significantly, give learning guarantees for the more common case of unbounded importance weights under the weak assumption that the second moment is bounded, a condition related to the Rényi divergence of the training and test distributions. These results are based on a series of novel and general bounds we derive for unbounded loss functions, which are of independent interest. We use these bounds to guide the definition of an alternative reweighting algorithm and report the results of experiments demonstrating its benefits. Finally, we analyze the properties of normalized importance weights which are also commonly used.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 23
Subtitle of host publication24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
StatePublished - 2010
Event24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada
Duration: Dec 6 2010Dec 9 2010

Publication series

NameAdvances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Other

Other24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
CountryCanada
CityVancouver, BC
Period12/6/1012/9/10

ASJC Scopus subject areas

  • Information Systems

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  • Cite this

    Cortes, C., Mansour, Y., & Mohri, M. (2010). Learning bounds for importance weighting. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).