Finding Landmarks of Covariate Shift with Max-Sliced Kernel Wasserstein Distance

TMLR Paper5139 Authors

Abstract: To detect and understand covariate shifts, especially those caused by localized changes in the distribution, we propose a more interpretable divergence through a kernel-based sliced Wasserstein divergence, which is computationally efficient for two-sample testing. The proposed landmark-based slicing seeks a single data point, defining a slice in the reproducing kernel Hilbert space, that maximizes the kernel max-sliced Wasserstein distance. This point and points that surround it from the two samples provide an interpretation of localized divergences. We investigate this new divergence on various shift scenarios and the effect of the choice of learning representations, compared to maximum mean discrepancy (MMD). Results on MNIST and CIFAR-10 dataset demonstrate superior statistical power of the divergence, and analysis of the landmark and its neighborhood are revealing about the discrepancy between the distributions.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Masashi_Sugiyama1

Submission Number: 5139