Title: On Recent Advances in Analysis of Markov Chains

Speaker: Kuikui Liu, Elting Morison Career Development Professor at MIT EECS

Abstract: Sampling from high-dimensional probability distributions is a fundamental and challenging problem encountered throughout science and engineering. One of the most ubiquitous approaches to tackle such problems is the Markov chain Monte Carlo (MCMC) paradigm. While MCMC algorithms are widely used in practice and often simple to implement, countless important problems remain wide open regarding their theoretical properties (e.g. rate of convergence to stationarity), as well as provable guarantees for other downstream tasks like optimization and statistical inference. In this talk, I will survey recent developments in the field, including unified frameworks for analyzing Markov chains based on spectral independence, localization schemes, and locally stationary distributions. These new techniques have led to the resolution of several decades-old conjectures. I will conclude with numerous open problems at the frontier of this research program.

Speaker Bio: Kuikui Liu is the Elting Morison Career Development Professor at MIT EECS. His research interests are in the design and analysis of sampling algorithms for high-dimensional probability distributions arising in statistical physics, Bayesian inference, theoretical computer science, and pure mathematics. He earned his PhD in computer science in 2022 from the University of Washington, before joining MIT as a Foundations of Data Science Institute postdoc and an assistant professor. He was the co-recipient of a best paper award at STOC 2019, the William Chan Memorial Dissertation Award in 2022, and the 2023 EATCS Distinguished Dissertation Award.