Muandet, K;
Sriperumbudur, B;
Fukumizu, K;
Gretton, A;
Schölkopf, B;
(2016)
Kernel Mean Shrinkage Estimators.
Journal of Machine Learning Research
, 17
, Article 48.
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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.
| Type: | Article |
|---|---|
| Title: | Kernel Mean Shrinkage Estimators |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://jmlr.org/papers/v17/14-195.html |
| Language: | English |
| Additional information: | Copyright © The authors. Licensed under a Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0). |
| Keywords: | covariance operator, James-Stein estimators, kernel methods, kernel mean, shrinkage estimators, Stein effect, Tikhonov regularization |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1522727 |
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