Sample Complexity of Probability Divergences under Group Symmetry

Published: 24 Apr 2023, Last Modified: 15 Jun 2023ICML 2023 PosterEveryoneRevisions
Abstract: We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized $\alpha$-divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories.
Submission Number: 2905
Loading

OpenReview is a long-term project to advance science through improved peer review with legal nonprofit status. We gratefully acknowledge the support of the OpenReview Sponsors. © 2025 OpenReview