Mathematics Colloquium
Jiaming Liang
University of Rochester
Title: Uniform, Constrained, and Composite Sampling via Proximal Sampler
Date: Friday, February 6th
Place and Time: Love 101, 3:05-3:55 pm
Abstract. This talk presents proximal algorithms for three log-concave sampling problems: uniform, constrained, and composite sampling. These problems form a natural hierarchy, where constrained sampling generalizes uniform sampling, and composite sampling further extends constrained sampling through more general potential structures arising in applications such as Bayesian inference. Our algorithm design is based on a sequence of reductions that connect the more general settings back to uniform sampling in suitable lifted spaces. At the core of our approach is an efficient and implementable proximal sampler for uniform sampling, which directly applies to the more general constrained and composite settings. For all three problems, we establish mixing time guarantees measured in Rényi and Chi-squared divergences.