SSD - Marzouk Seminar
Prof. Youssef Marzouk, Ph.D. - Transport Methods for Sampling: Preconditioning and Low-dimensional Structure
Department of Aeronautics and Astronautics,Massachusetts Institute of Technology, USA
Integration against an intractable probability measure is a fundamental challenge in Bayesian inference and well beyond. A useful approach to this problem seeks a deterministic coupling of the measure of interest with a tractable “reference” measure (e.g., a standard Gaussian). Such couplings are induced by transport maps, and enable direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. In recent years, an enormous variety of representations and constructions for such transport maps have been proposed—ranging from monotone polynomials or invertible neural networks to the flows of ODEs. Approximate transports can also be used to “precondition” and accelerate standard Monte Carlo schemes. Within this framework, one can describe many useful notions of low-dimensional structure: for instance, sparse or decomposable transports underpin modeling and computation with non-Gaussian Markov random fields, and low-rank transports arise frequently in inverse problems.
I will present a broad overview of this framework, describing how to construct suitable classes of transport maps, and then focus on two recent developments: adaptive MCMC schemes that use transport to create more favorable target geometry, and greedy variational methods that build high-dimensional transport maps by composing multiple low-dimensionalmaps or flows.
This is joint work with Daniele Bigoni, Matthew Parno, Alessio Spantini, and Olivier Zahm.
Speaker bio: Youssef Marzouk is an associate professor in the Department of Aeronautics and Astronautics at MIT, and co-director of the MIT Center for Computational Engineering. He is also director of MIT’s Aerospace Computational Design Laboratory and a core member of MIT's Statistics and Data Science Center. His research interests lie at the intersection of physical modeling with statistical inference and computation. In particular, he develops methodologies for uncertainty quantification, inverse problems, large-scale Bayesian computation, and optimal experimental design in complex physical systems. His methodological work is motivated by a wide variety of engineering, environmental, and geophysics applications. He received his SB, SM, and PhD 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 is an Associate Fellow of the AIAA and currently serves on the editorial boards of the SIAM Journal on Scientific Computing, Advances in Computational Mathematics, and the SIAM/ASA Journal on Uncertainty Quantification, among other journals. He is also an avid coffee drinker and occasional classical pianist.