Kernel Mean Estimation by Marginalized Corrupted Distributions
This work addresses a critical component in kernel learning algorithms, offering an incremental improvement over existing shrinkage methods for researchers and practitioners in machine learning.
The paper tackles the problem of kernel mean estimation in reproducing kernel Hilbert spaces by proposing a marginalized kernel mean estimator that corrupts data with noise from known distributions, achieving significantly lower estimation error across various datasets.
Estimating the kernel mean in a reproducing kernel Hilbert space is a critical 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 by shrinkage methods. In this work, we propose to corrupt data examples with noise from known distributions and present a new kernel mean estimator, called the marginalized kernel mean estimator, which estimates kernel mean under the corrupted distribution. Theoretically, we show that the marginalized kernel mean estimator introduces implicit regularization in kernel mean estimation. Empirically, we show on a variety of datasets that the marginalized kernel mean estimator obtains much lower estimation error than the existing estimators.