Statistics Webinar

(2022-07)

Topic:Optimal Transport: Theory and Applications

Speaker:Nian Si, Stanford University

Time:Thursday, October 27, 2:00 - 4:00 p.m. Beijing Time

Location:Tencent Meeting

Abstract

Optimal transport has gained increasing attention in recent years due to the modeling power and computational tractability. In this talk, I will first study the duality of optimal transport for discrete probability measures and extend to continuous probability measures. Then, I will talk about the optimization to solve optimal transport problems via the Sinkhorn methods. I will also study the statistical properties of optimal transport: the curse of dimensionality. I will present two ideas to beat the curse of dimensionality: projection and smoothing. Finally, I will discuss two applications: Wasserstein GANs and distributionally robust optimization.

Introduction

Nian Si

Nian Si is a final-year PhD student in the Department of Management Science and Engineering (MS&E) at Stanford University, where he is advised by Professor Jose Blanchet. He is a member of the Stanford Operations Research Group. Previously, he obtained a B.A. in Economics and a B.S. in Mathematics and Applied Mathematics both from Peking University in 2017.

His research lies at the interface of applied probability and machine learning. He develops methods for trustworthy decision making, especially for settings under distributional shifts.