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Estimating the kernel mean in a reproducing kernel Hilbert space is acritical component in many kernel learning algorithms. Given a finite sample,the standard estimate of the target kernel mean is the empirical average.Previous works have shown that better estimators can be constructed byshrinkage methods. In this work, we propose to corrupt data examples with noisefrom known distributions and present a new kernel mean estimator, called themarginalized kernel mean estimator, which estimates kernel mean under thecorrupted distribution. Theoretically, we show that the marginalized kernelmean estimator introduces implicit regularization in kernel mean estimation.Empirically, we show on a variety of datasets that the marginalized kernel meanestimator obtains much lower estimation error than the existing estimators.

Kernel Mean Estimation by Marginalized Corrupted Distributions