TY - GEN

T1 - Kernel mean estimation and stein effect

AU - Muandet, Krikamol

AU - Fukumizu, Kenji

AU - Sriperumbudur, Bharath

AU - Gretton, Arthur

AU - Schölkopf, Bernhard

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84919825014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919825014&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84919825014

T3 - 31st International Conference on Machine Learning, ICML 2014

SP - 12

EP - 36

BT - 31st International Conference on Machine Learning, ICML 2014

PB - International Machine Learning Society (IMLS)

T2 - 31st International Conference on Machine Learning, ICML 2014

Y2 - 21 June 2014 through 26 June 2014

ER -