  A mean function in reproducing kernel Hilbert space, or a kernel mean, is an
important part of many applications ranging from kernel principal component
analysis to Hilbert-space embedding of distributions. Given finite samples, an
empirical average is the standard estimate for the true kernel mean. We show
that this estimator can be improved via 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. Focusing on a subset of this class, we propose efficient shrinkage
estimators for the kernel mean. Empirical evaluations on several benchmark
applications clearly demonstrate that the proposed estimators outperform the
standard kernel mean estimator.
