Sampling from Graphical Models via Spectral Independence

Title: Sampling from Graphical Models via Spectral Independence

Abstract: In many scientific settings we use a statistical model to describe a high-dimensional distribution over many variables. Such models are often represented as a weighted graph encoding the dependencies between different variables and are known as graphical models. Graphical models arise in a wide variety of scientific fields throughout science and engineering. 

One fundamental task for graphical models is to generate random samples from the associated distribution. The Markov chain Monte Carlo (MCMC) method is one of the simplest and most popular approaches to tackle such problems. Despite the popularity of graphical models and MCMC algorithms, theoretical guarantees of their performance are not known even for some simple models. I will describe a new tool called "spectral independence" to analyze MCMC algorithms and more importantly to reveal the mathematical nature behind such models. I will also discuss how these structural properties can be applied to sampling when MCMC fails and to other statistical problems like parameter learning or model fitting.

Bio: Zongchen Chen is an instructor (postdoc) in Mathematics at MIT. He received his Ph.D. degree in Algorithms, Combinatorics and Optimization (ACO) at Georgia Tech in 2021 advised by Eric Vigoda. His thesis received the 2021 Georgia Tech College of Computing Outstanding Doctoral Dissertation Award. He received his BS degree in Mathematics & Applied Mathematics from Zhiyuan College at Shanghai Jiao Tong University in 2016. He is broadly interested in randomized algorithms, discrete probability, and machine learning. His current research interests include Markov chain Monte Carlo (MCMC) methods, approximate counting and sampling, and learning and testing for high-dimensional distributions.