Tuesday, April 30, 2019 - 4:00pm to Wednesday, May 1, 2019 - 4:55pm
Event Calendar Category
LIDS Seminar Series
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Bayesian inference for non-Gaussian state-space models is a ubiquitous problem with applications ranging from geophysical data assimilation to mathematical finance. We will discuss how deterministic couplings between probability distributions enable new solutions to this problem.
We first consider filtering in high-dimensional models with nonlinear (potentially chaotic) dynamics and sparse observations in space and time. While the ensemble Kalman filter (EnKF) yields robust ensemble approximations of the filtering distribution in this setting, it is limited by linear forecast-to-analysis transformations. To generalize the EnKF, we propose a methodology that transforms the non-Gaussian forecast ensemble at each assimilation step into samples from the current filtering distribution via a sequence of local nonlinear couplings. These couplings are based on transport maps that can be computed quickly using convex optimization, and that can be enriched in complexity to reduce the intrinsic bias of the EnKF. We discuss the low-dimensional structure inherited by the transport maps from the filtering problem, including decay of correlations, conditional independence, and local likelihoods. We then exploit this structure to regularize the estimation of the maps in high dimensions and with a limited ensemble size.
We also present variational methods---again based on transport---for smoothing and sequential parameter estimation in non-Gaussian state-space models. These methods rely on results linking the Markov properties of a target measure to the existence of low-dimensional couplings, induced by transport maps that are decomposable. The resulting algorithms can be understood as a generalization, to the non-Gaussian case, of the square-root Rauch--Tung--Striebel Gaussian smoother.
This is joint work with Ricardo Baptista, Daniele Bigoni, and Alessio Spantini.
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 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. He is an avid coffee drinker and occasional classical pianist.