On Regularisation of Maximum Mean Discrepancy Gradient Flow: From Dr. to Sr. by Dr Zonghao Chen

Abstract

Maximum Mean Discrepancy (MMD) gradient flows provide a tractable particle-based approach to transporting distributions using kernels, but their convergence can be hindered by the non-convex geometry of the MMD objective. This talk introduces two complementary regularizations to address this limitation.

The first, de-regularized MMD (DrMMD), interpolates between MMD and χ²-divergence, yielding near-global convergence guarantees under isoperimetric assumptions and motivating an adaptive de-regularization schedule. The second, Sobolev-regularized MMD (SrMMD), penalizes the gradient norm of the MMD witness function, achieving global convergence without requiring isoperimetric assumptions. Instead, it relies on regularity between kernel mean embeddings. Together, these approaches provide a flexible framework for generative modeling and sampling, combining the computational tractability of kernel methods with stronger convergence guarantees.

Biography

Zonghao Chen is an incoming postdoctoral researcher at the University of Pennsylvania, where he will work with Weijie Su. He is currently completing his Ph.D. at the Centre for Foundational Artificial Intelligence, University College London (UCL) under the supervision of François-Xavier Briol and Arthur Gretton.

His research focuses on understanding machine learning algorithms from the perspectives of optimization and generalization, with particular interests in generative models, Monte Carlo methods, and causal inference. He received his Bachelor's degree in Electronic Engineering from Tsinghua University in 2022.