Title: Sampling and generative modeling using dynamical representations of transport

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. We will attempt to illuminate the  pitfalls and opportunities of these dynamical methods.

Bio: Youssef Marzouk is the Breene M. Kerr (1951) Professor of 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 core member of MIT's Statistics and Data Science Center and a PI in the MIT Laboratory for Information and Decision Systems (LIDS). His research interests lie at the intersection of statistical inference, computational mathematics, 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 inference, with applications to data assimilation and inverse problems; dimension reduction methodologies 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 an avid coffee drinker and an occasional classical pianist.