11:30 am–12:30 pm
Jones 303 5747 S Ellis Avenue
Monday, October 20, 2025 at 11:30 AM in Jones 303, 5747 S Ellis Ave.
Zhou Fan, Department of Statistics and Data Science, at Yale University
Title: “Empirical Bayes Langevin dynamics in the linear model”
Abstract: In many applications of statistical estimation via sampling, one may wish to sample from a highdimensional target distribution that is adaptively evolving to the samples already seen. I will present an example of such dynamics in a Bayesian linear model, given by a Langevin diffusion for sampling from a posterior distribution that adapts to implement empirical Bayes learning of the prior. In this talk, I hope to discuss a positive result on nonparametric consistency for this empirical Bayes learning task, a motivation of these dynamics from a perspective of Wasserstein gradient flows, and a precise characterization of the dynamics in a mean-field setting of i.i.d. regression design.
Based on joint work with Yandi Shen, Leying Guan, Justin Ko, Bruno Loureiro, Yue M. Lu, and Yihong Wu.