\dm_csml_event_details UCL ELLIS

Explicit convergence bounds for Metropolis Markov chains


Sam Power


University of Bristol


Friday, 17 February 2023




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


Markov chain Monte Carlo (MCMC) algorithms are a widely-used tool for approximate simulation from probability measures in structured, high-dimensional spaces, with a variety of applications. A key ingredient of their success is their ability to converge rapidly to equilibrium at a rate which depends acceptably on the ‘difficulty' of the sampling problem at hand, as captured by the dimension of the problem, and the concentration and smoothness properties of the target distribution. In this talk, I will present recent work with C. Andrieu, A. Lee and A. Wang on the convergence analysis of Metropolis-type MCMC algorithms on R^d. In particular, we provide a detailed study of the Random Walk Metropolis (RWM) Markov chain with arbitrary proposal variances and in any dimension, obtaining interpretable estimates on their convergence behaviour under suitable assumptions. These estimates have a provably sharp dependence on the dimension of the problem, thus providing theoretical validation for the use of these algorithms in complex settings. Our positive results are quite generally applicable. We also study the preconditioned Crank--Nicolson Markov chain as applied to simulation from Gaussian Process posterior models, obtaining dimension-independent complexity bounds under suitable assumptions.


Sam Power is a researcher in Statistics. He is currently a Postdoctoral Research Associate at the University of Bristol, working with Prof. Christophe Andrieu on the Bayes4Health grant. He also works closely with Prof. Anthony Lee at Bristol. Prior to this role, he was a PhD student at the University of Cambridge, working with Dr. Sergio Bacallado. His research interests center around the design and analysis of stochastic algorithms, with applications mainly to statistics. I am particularly interested in Monte Carlo methods, such as Markov Chain Monte Carlo and Sequential Monte Carlo, and how the implementation of these methods can be made automatic, robust, and efficient.