Kernel mean estimation and stein effect

Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Arthur Gretton, Bernhard Schölkopf

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

9 Scopus citations

Abstract

2014 A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is an important part of many algorithms ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given a finite sample, an empirical average is the standard estimate for the true kernel mean. We show that this estimator can be improved due to a well-known phenomenon in statistics called Stein's phenomenon. After consideration, our theoretical analysis reveals the existence of a wide class of estimators that are better than the standard one. Focusing on a subset of this class, we propose efficient shrinkage estimators for the kernel mean. Empirical evaluations on several applications clearly demonstrate that the proposed estimators outperform the standard kernel mean estimator.

Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages12-36
Number of pages25
ISBN (Electronic)9781634393973
StatePublished - Jan 1 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: Jun 21 2014Jun 26 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume1

Other

Other31st International Conference on Machine Learning, ICML 2014
CountryChina
CityBeijing
Period6/21/146/26/14

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All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

Cite this

Muandet, K., Fukumizu, K., Sriperumbudur, B., Gretton, A., & Schölkopf, B. (2014). Kernel mean estimation and stein effect. In 31st International Conference on Machine Learning, ICML 2014 (pp. 12-36). (31st International Conference on Machine Learning, ICML 2014; Vol. 1). International Machine Learning Society (IMLS).