Kernel mean shrinkage estimators

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

Research output: Contribution to journalReview article

15 Scopus citations

Abstract

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference step of modern kernel methods that rely on embedding probability distributions in RKHSs. Given a finite sample, an empirical average has been used commonly as a standard estimator of the true kernel mean. Despite a widespread use of this estimator, we show that it can be improved thanks to the well-known Stein phenomenon. We propose a new family of estimators called kernel mean shrinkage estimators (KMSEs), which benefit from both theoretical justifications and good empirical performance. The results demonstrate that the proposed estimators outperform the standard one, especially in a "large d, small n" paradigm.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume17
StatePublished - Apr 1 2016

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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    Muandet, K., Sriperumbudur, B., Fukumizu, K., Gretton, A., & Schölkopf, B. (2016). Kernel mean shrinkage estimators. Journal of Machine Learning Research, 17.