Talk Title

Error Lower Bounds for Approximate MCMC

Abstract

It is widely known that the performance of MCMC algorithms can degrade quite quickly when targeting computationally expensive posterior distributions, including the posteriors associated with any large dataset. This has motivated the search for MCMC variants that scale well for large datasets. One general approach is to look at only a subsample of the data at every step. In this talk, we give error lower bounds that provide some basic limits on the performance of many such algorithms. We apply these generic results to realistic statistical problems and proposed algorithms, and also discuss some special examples that can avoid our generic results. (Based on work with James Johndrow, Natesh Pillai, Pengfei Wang, and Azeem Zaman.)

Bio

Aaron Smith is Associate Professor of Mathematics and Statistics at the University of Ottawa. His academic work is focused on applied probability, computational statistics, and especially the theory of Markov chain Monte Carlo methods. He is currently an editor of SIAM: Mathematics of Data Science. His work has been funded through a variety of national bodies including NSERC, MITACS, and DRDC. Between receiving his PhD in mathematics in 2012 and joining the University of Ottawa, Aaron worked in industry as a researcher on applied problems in machine learning; he continues to work on both academic and industrial projects.