题目：Approximate Bayesian Computation via Variational Approximation

主讲人：伊利诺伊大学香槟分校 杨运助理教授

主持人：统计学院 常晋源教授

时间：2021年11月12日（周五）上午10:00-11:00

地点：腾讯会议，661 465 039

报告摘要：

Variational inference is a popular alternative to Markov Chain Monte Carlo (MCMC) for approximating complicated probability densities arising from Bayesian hierarchical models. However, unlike MCMC that is guaranteed to produce precise samples from the target density for ergodic chains, theoretical aspects of VI is less explored in the literature. In this talk, we will discuss our recent progress towards theoretical understanding of VI. In the first part of the talk, we provide general conditions under which VI is consistent for point estimation and model selection under a frequentist setup. However, it is a well-known fact that variational procedures tend to underestimate the variability of the target posterior distributions, leading to incorrect uncertainty quantification. In the second part of the talk, we study the distributional convergence of VI for parameter models, based on which we propose a multiplier bootstrap method for valid uncertainty quantification in mean-field variational approximation.

主讲人简介：

Yun Yang received B.S. degree in mathematics from Tsinghua University, China, in 2011, and Ph.D. degree in statistics from Duke University, USA, in 2014. From 2014 to 2016, he was a Post-Doctoral Researcher with the University of California, Berkeley, USA, working on problems in machine learning, optimization, and high-dimensional statistics. From 2016 to 2018, he was an Assistant Professor in statistics with the Florida State University. He is currently an Assistant Professor in statistics with the University of Illinois Urbana-Champaign. His current research interests include Bayesian inference, high-dimensional statistics, machine learning and nonparametric statistics.