Dr Xiaohui Chen from the University of Southern California will be discussing about "Recent progress in statistical and computational optimal transport barycenters" on Wednesday November 19 in HSSB 1173 from 3:30 - 4:30pm.
Title:
Recent progress in statistical and computational optimal transport barycenters
Abstract:
The Wasserstein barycenter plays a fundamental role in averaging measure-valued data under the framework of optimal transport (OT). However, there are tremendous challenges in computing and estimating the Wasserstein barycenter for high-dimensional distributions. In this talk, we will discuss some recent progress in advancing the statistical and computational frontiers of optimal transport barycenters. We first introduce a multimarginal Schrödinger barycenter (MSB) based on the entropy regularized multimarginal optimal transport problem that admits general-purpose fast algorithms for computation. By recognizing a proper dual geometry, we derive sharp non-asymptotic rates of convergence for estimating several key MSB quantities (cost functional, Schrödinger coupling and barycenter) from point clouds randomly sampled from the input marginal distributions. We will also consider the computation exact (i.e., unregularized) Wasserstein barycenter, which can be recast into a nonconvex-concave minimax optimization. By alternating between the primal Wasserstein and dual potential Sobolev optimization geometries, we introduce a linear-time and linear-space Wasserstein-Descent H-Ascent (WDHA) algorithm and prove its algorithmic convergence to a stationary point. Time permitting, we will talk about a pure unconstrained concave formulation of the barycenter problem and its associated Sobolev gradient descent algorithm.
Joint work with Pengtao Li (USC), Rentian Yao (UBC), Changbo Zhu (Notre Dame), Kaheon Kim (Notre Dame), Bohan Zhou (UC Santa Barbara)
About:
Xiaohui Chen is an Associate Professor of Mathematics at the University of Southern California (USC). He was an Associate Professor of Statistics from 2019-2023 and an Assistant Professor of Statistics from 2013-2019 at the University of Illinois, Urbana-Champaign (UIUC). In 2019-2020 he was a Visiting Faculty in the Institute for Data, Systems, and Society (IDSS) at Massachusetts Institute of Technology (MIT). His research work lies at the intersection of statistical machine learning and optimization.
Dr. Chen received a Ph.D. in Electrical and Computer Engineering in 2013 from the University of British Columbia (UBC), Vancouver, Canada. He was a post-doctoral fellow at the Toyota Technological Institute at Chicago (TTIC), a philanthropically endowed academic computer science institute located on the University of Chicago campus. He received numerous notable research awards, including an NSF CAREER Award in 2018, an Arnold O. Beckman Award at UIUC in 2018, an ICSA Outstanding Young Researcher Award in 2019, an Associate appointment in the Center for Advanced Study at UIUC in 2020-2021, and a Simons Fellowship in Mathematics from the Simons Foundation in 2020-2021.