Time: 4:30-5:30 p.m.
Date: Wednesday, October 1, 2025
Speaker: Chenyang Zhong
Title: Variational Inference for Latent Variable Models in High Dimensions
Abstract: Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this talk, I will present a novel framework for quantifying the statistical accuracy of mean-field variational inference (MFVI) for posterior approximation in Bayesian latent variable models with categorical local latent variables. We apply the general framework to two important latent variable models: the latent Dirichlet allocation (LDA) model and the mixed membership stochastic blockmodel (MMSB). For the celebrated LDA model, we characterize the exact regime where MFVI is accurate and derive its optimal finite-sample rate of convergence. For MMSB, we show that the vanilla fully factorized MFVI, often used in the literature, is suboptimal. To address this, we propose a partially grouped VI algorithm for this model and show that it works, and derive its exact finite-sample performance. Our proof techniques, which extend the framework of nonlinear large deviations, open the door for the analysis of MFVI in other latent variable models.
This is joint work with Sumit Mukherjee and Bodhisattva Sen.
Bio: Chenyang Zhong is an Assistant Professor in the Department of Statistics at Columbia University. He received his Ph.D. in Statistics from Stanford University, advised by Persi Diaconis. His research lies at the intersection of statistics and applied probability, with a focus on Markov chain Monte Carlo, variational inference, and optimal transport.