BIDS Machine Learning and Science Forum
Date: Monday, May 2, 2022
Time: 11:00 AM - 12:00 PM Pacific Time
Location: Participate remotely using this Zoom link
Transport methods for stochastic modeling and inference
Speaker: Youssef M. Marzouk, Professor of Aeronautics and Astronautics at MIT, Co-director of the MIT Center for Computational Science and Engineering
Abstract: Transportation of measure underlies many powerful tools for Bayesian inference, density estimation, and stochastic modeling. A central idea is to deterministically couple a probability 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, invertible neural networks, and normalizing flows to the flows of ODEs. 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 an overview of this framework, and then focus on new developments for nonlinear ensemble filtering and likelihood-free inference (LFI). Some of the associated algorithms can be understood as the natural nonlinear generalization of the ensemble Kalman filter. Motivated by broader applications in LFI and generative modeling, I will also discuss methods for estimating monotone triangular maps from few samples, and joint dimension reduction of parameters and data in inference applications.
The BIDS Machine Learning and Science Forum meets biweekly to discuss current applications across a wide variety of research domains in the physical sciences and beyond. Hosted by BIDS Affiliates Uroš Seljak (professor of Physics at UC Berkeley) and Ben Nachman (physicist at Lawrence Berkeley National Laboratory), these active sessions bring together domain scientists, statisticians, and computer scientists who are either developing state-of-the-art methods or are interested in applying these methods in their research. To receive email notifications about upcoming meetings, or to request more information, please contact the organizers at berkeleymlforum@gmail.com. All interested members of the UC Berkeley and Berkeley Lab communities are welcome and encouraged to attend.
Speaker(s)
Youssef M Marzouk
Youssef Marzouk is a Professor in the Department of Aeronautics and Astronautics at MIT, and co-director of the MIT Center for Computational Science and Engineering, within the MIT Schwarzman College of Computing. He is also a core member of MIT's Statistics and Data Science Center. His research interests lie at the intersection of computation and statistical inference with physical modeling. With his students and collaborators, he has developed new methodologies for uncertainty quantification, Bayesian modeling and computation, data assimilation, optimal experimental design, and machine learning—motivated by a wide variety of engineering and science applications. He received SB, SM, and PhD degrees from MIT and spent four years at Sandia National Laboratories before joining the MIT faculty in 2009. He is a recipient of the Hertz Foundation Doctoral Thesis Prize, the Sandia Laboratories Truman Fellowship, the US Department of Energy Early Career Research Award, and the Junior Bose Award for Teaching Excellence from the MIT School of Engineering. He is an Associate Fellow of the AIAA and currently serves on the editorial boards of the SIAM Journal on Scientific Computing, the SIAM/ASA Journal on Uncertainty Quantification, and several other journals.