A1879
Title: Lipschitz-regularized probability divergences and applications to generative modeling
Authors: Ziyu Chen - University of North Carolina at Chapel Hill (United States) [presenting]
Abstract: Probability divergences such as the Kullback-Leibler (KL) divergence provide an information-theoretic measure of discrepancy between two probability distributions, but they require absolute continuity of one distribution with respect to the other. This assumption often fails for empirical measures or distributions supported on low-dimensional structures. In contrast, Wasserstein metrics quantify the transport cost between distributions without requiring absolute continuity, but they can break down when one of the distributions is heavy-tailed. Lipschitz-regularized divergences, introduced as a special class of (f, Gamma)-divergences, combine f-divergences and the Wasserstein-1 metric via their variational (dual) formulations and inherit the advantages of both. Key theoretical properties of Lipschitz-regularized f-divergences are presented, demonstrating how these results lead to robust generative modeling methods under minimal assumptions on the target data distribution, including cases with heavy tails, low-dimensional structure, or fractal-like support.
