Learning in Hilbert vs. Banach spaces: A measure embedding viewpoint

Bharath K. Sriperumbudur, Kenji Fukumizu, Gert R.G. Lanckriet

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

19 Scopus citations

Abstract

The goal of this paper is to investigate the advantages and disadvantages of learning in Banach spaces over Hilbert spaces. While many works have been carried out in generalizing Hilbert methods to Banach spaces, in this paper, we consider the simple problem of learning a Parzen window classifier in a reproducing kernel Banach space (RKBS)-which is closely related to the notion of embedding probability measures into an RKBS-in order to carefully understand its pros and cons over the Hilbert space classifier. We show that while this generalization yields richer distance measures on probabilities compared to its Hilbert space counterpart, it however suffers from serious computational drawback limiting its practical applicability, which therefore demonstrates the need for developing efficient learning algorithms in Banach spaces.

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 - 2011
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
Country/TerritorySpain
CityGranada
Period12/12/1112/14/11

All Science Journal Classification (ASJC) codes

  • Information Systems

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