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(De)-regularized maximum mean discrepancy gradient flow

Series: Department Seminar

Speaker: Prof. Bharath Sriperumbudur, Professor, Department of Statistics (with a courtesy appointment in the Department of Mathematics), Pennsylvania State University

Date/Time: Dec 15 10:00:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

Abstract:
We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from the source distribution to the target distribution with only target samples either lack tractable numerical implementation (f-divergence flows) or require strong assumptions, and modifications such as noise injection, to ensure convergence (Maximum Mean Discrepancy flows). In contrast, DrMMD flow can simultaneously (i) guarantee near-global convergence for a broad class of targets in both continuous and discrete time, and (ii) be implemented in closed form using only samples. The former is achieved by leveraging the connection between the DrMMD and the chi^2-divergence, while the latter comes by treating DrMMD as MMD with a de-regularized kernel. Our numerical scheme uses an adaptive de-regularization schedule throughout the flow to optimally trade off between discretization errors and deviations from the chi^2 regime. The potential application of the DrMMD flow is demonstrated across several numerical experiments, including a large-scale setting of training student/teacher networks.

Speaker Bio:
Bharath Sriperumbudur is a faculty member in the Department of Statistics, with a courtesy appointment in the Department of Mathematics, at the Pennsylvania State University. His research spans non-parametric statistics, machine learning, statistical learning theory, optimal transport and gradient flows, regularization and inverse problems, and the study of reproducing kernel spaces in probability and statistics. He also works extensively in functional and topological data analysis. His current research is supported by the NSF-DMS CAREER award 1945396, -Statistical Learning, Inference and Approximation with Reproducing Kernels.-

Host Faculty: Prof. Anant Raj