Speaker: Yifan Chen, Courant Institute

Title: Fast, Multimodal, and Derivative-Free Bayes Inference with Fisher-Rao Gradient Flows

Abstract: Sampling from a target distribution with an unknown normalization constant is a fundamental challenge in computational science. A common algorithmic approach for sampling involves designing a dynamical system of distributions that gradually converge to the target. Simulating these dynamics can then sample. Examples include sequential Monte Carlo, MCMC, and also gradient flows in the probability space that has become popular in recent decades. In this talk, I will discuss how the Fisher-Rao gradient flow of the KL divergence emerges as a fast and unique dynamical system within the broad category of gradient flows for sampling. I will focus on applications in large-scale Bayes inverse problems where model evaluations are expensive, posteriors can be multimodal, and the gradient information may be infeasible. We address these challenges by simulating Fisher-Rao gradient flows with Gaussian mixture approximations and Kalman’s methodology, which result in a fast, multimodal, and derivative-free sampler that we will provide theoretical insights and numerical experiments to justify its effectiveness.

Bio: Yifan Chen is a Courant instructor at the Courant Institute, New York University. He obtained his Ph.D. in applied and computational mathematics from Caltech in 2023, working under the supervision of Thomas Hou, Houman Owhadi, and Andrew Stuart. Prior to Caltech, he obtained his bachelor’s degree in pure and applied mathematics from Tsinghua University. Yifan’s research interests lie in mathematics of heterogeneous or high-dimensional computational and learning problems in partial differential equations and data science. He particularly focuses on topics in multiscale methods, kernel methods, randomized algorithms, and dynamical sampling.

This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to cr2090@columbia.edu.