Description:

ABSTRACT: Drawing samples from a probability distribution is a central task in applied mathematics, statistics, and machine learning—with applications ranging from Bayesian inference to computational chemistry and generative modeling. Many powerful tools for sampling employ transportation of measure, where the essential idea is to couple the target probability distribution with a simple, tractable “reference" distribution, and to use this coupling (which may be deterministic or stochastic) to generate new samples.

Within this broad area, an emerging class of methods use dynamics to define a transport incrementally, e.g., via the flow map induced by trajectories of an ODE. These methods have shown great empirical success, but their consistency and convergence properties, and the ways in which they can exploit structure in the underlying distributions, are less well understood.  We will discuss properties and theoretical underpinnings of these dynamical approaches to transport. In particular, we will discuss the statistical convergence of generative models based on neural ODEs. We will also present a new dynamical construction of transport: a gradient-free method which avoids complex training procedures by instead evolving an interacting particle system that approximates a Fisher–Rao gradient flow. Finally, we will discuss aspects of the "optimal scheduling" problem for dynamic transport, illustrating how to exploit the flexibility afforded by the time-dependent setting.

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BIO:  Youssef Marzouk is the Breene M. Kerr (1951) Professor in Aeronautics and Astronautics at the Massachusetts Institute of Technology (MIT), and co-director of the Center for Computational Science and Engineering within the MIT Schwarzman College of Computing. He is also a PI in the MIT Laboratory for Information and Decision Systems (LIDS) and a core member of MIT's Statistics and Data Science Center. His research interests lie at the intersection of computational mathematics, statistical inference, and physical modeling. He develops new methodologies for uncertainty quantification, Bayesian computation, and machine learning in complex physical systems, motivated by a broad range of engineering and science applications. His recent work has centered on algorithms for data assimilation and inverse problems; dimension reduction for high-dimensional learning and surrogate modeling; optimal experimental design; and transportation of measure. He received his 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 fellow of SIAM, an avid coffee drinker, and an occasional classical pianist.