Time: Refreshments from 16:00, Talk around 16:30 (duration of seminar 1h).
Non-members welcome (as always).
Location: Room E-410 (Room 410 in E-block) at the Gardens Point Campus, Queensland University of Technology
Members and guests are welcome to join the speaker afterwards at a nearby restaurant.
Speaker: Youssef Marzouk
Title: Put transport in your toolbox: maps for Bayesian computation
Abstract: Integration against an intractable probability measure is among the fundamental challenges of statistical inference, particularly in the Bayesian setting. We discuss how deterministic couplings of probability measures, induced by transport maps, can enable useful new approaches to this problem.
A first approach involves a combination of transport maps and Metropolis correction; here, we use nonlinear maps to transform typical MCMC proposals into adapted non-Gaussian proposals. Second, we discuss a variational inference method that constructs a deterministic transport map from a reference distribution to the posterior, without resorting to MCMC. Independent and unweighted samples can then be obtained by pushing forward reference samples through the map. Making either approach efficient in high dimensions, however, requires identifying and exploiting low-dimensional structure. We present new results relating the sparsity and decomposability of transports to the conditional independence structure of the target distribution. We also describe conditions, common in inverse problems, under which transport maps have a particular low-rank structure. In general, these properties of transports can yield more efficient algorithms. As a particular example, we propose new variational algorithms for online inference in nonlinear and non-Gaussian state-space models with static parameters. Other illustrative applications involve spatial statistics and partial differential equations.
This is joint work with Daniele Bigoni, Matt Parno, and Alessio Spantini.
Biography: Youssef Marzouk is an associate professor in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology (MIT), and Director of MIT’s Aerospace Computational Design Laboratory. He is also co-director of educational programs for the MIT Center for Computational Engineering and a member of MIT’s new Statistics and Data Science Center. His research focuses on uncertainty quantification, inverse problems, statistical inference, and large-scale Bayesian computation for complex physical systems, and on using these approaches in energy conversion and environmental applications. He received his SB (1997), SM (1999), and PhD (2004) degrees from MIT, and spent several years at Sandia National Laboratories before joining the MIT faculty in 2009. He is a recipient of the Hertz Foundation Doctoral Thesis Prize (2004), the Sandia Laboratories Truman Fellowship (2004-2007), the US Department of Energy Early Career Research Award (2010), and the Junior Bose Award for Teaching Excellence from the MIT School of Engineering (2012). He serves on the editorial boards of several journals, including the SIAM Journal on Scientific Computing, Advances in Computational Mathematics, and the SIAM/ASA Journal on Uncertainty Quantification.
|Time:||4:00 pm - 5:30 pm|