Kernel mean estimation via spectral filtering

Krikamol Muandet, Bharath Kumar Sriperumbudur, Bernhard Schölkopf

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations

Abstract

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Previous work [1] has shown that shrinkage can help in constructing "better" estimators of the kernel mean than the empirical estimator. The present paper studies the consistency and admissibility of the estimators in [1], and proposes a wider class of shrinkage estimators that improve upon the empirical estimator by considering appropriate basis functions. Using the kernel PCA basis, we show that some of these estimators can be constructed using spectral filtering algorithms which are shown to be consistent under some technical assumptions. Our theoretical analysis also reveals a fundamental connection to the kernel-based supervised learning framework. The proposed estimators are simple to implement and perform well in practice.

Original languageEnglish (US)
Pages (from-to)1-9
Number of pages9
JournalAdvances in Neural Information Processing Systems
Volume1
Issue numberJanuary
StatePublished - Jan 1 2014
Event28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada
Duration: Dec 8 2014Dec 13 2014

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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