Widely Applied Mathematics presents...

"Sampling and Generative Modeling Using Dynamical Representations of Transport"

Professor Youssef Marzouk, Massachusetts Institute of Technology

Thursday, October 31
2:00 - 3:00pm
Pierce 301

Drawing samples from a probability distribution is a central task in applied mathematics, statistics, and machine learning—with applications ranging from Bayesian computation 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 new 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 relative advantages and pitfalls of these dynamical methods, and the many design choices that they entail.

Speaker: 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. He is also a core member of MIT’s Statistics and Data Science Center and director of MIT’s Aerospace Computational Design Laboratory. His research interests lie at the intersection of computation and statistical inference with physical modeling. He develops new methodologies for uncertainty quantification, Bayesian modeling and computation, data assimilation, experimental design, and machine learning in complex physical systems. His methodological work is motivated by a wide variety of engineering and environmental applications. He is an avid coffee drinker and occasional classical pianist.