Abstract: Generative models, including generative adversarial networks (GANs), optimal transport maps, and diffusion models, have achieved remarkable success at sampling from complex high-dimensional distributions. The Bayesian update in filtering is itself a conditional sampling problem: given a new observation, transform samples from the predicted distribution into samples from the posterior. This raises a natural question: can generative models be repurposed as filtering algorithms, overcoming the Gaussian assumption of Kalman-type filters and the degeneracy of particle filters in high dimensions?
In this talk, Professor Taghvaei will focus on one such construction, based on conditional optimal transport theory, in which the Bayesian update is realized as a transport map obtained by solving a conditional Kantorovich problem. Taghvaei will present the algorithm, provide an error analysis for the estimation of conditional optimal transport maps, describe algorithmic developments that accelerate computation, and offer an empirical comparison with filters built from other generative models.
Biography: Amirhossein Taghvaei is an assistant professor in the William E. Boeing Department of Aeronautics & Astronautics at the University of Washington. His research lies at the intersection of control theory, statistical inference, and machine learning, with a focus on principled, scalable methods for decision-making under uncertainty. He received his doctoral degree from the University of Illinois Urbana-Champaign and was a postdoctoral scholar at the University of California, Irvine. He is a recipient of the AFOSR Young Investigator Program (YIP) award, and his work has appeared in leading control and machine learning venues, including IEEE TAC, ICML, and NeurIPS.
