arxiv:2302.01915

Sample Complexity of Probability Divergences under Group Symmetry

Published on Feb 3, 2023

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Abstract

The study quantifies sample complexity reduction in variational divergence estimations for group-invariant distributions, showing improvements proportional to the group size for specific divergences, with MMD results depending on the choice of kernel.

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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.

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