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DTSTART;TZID=America/Los_Angeles:20260209T140000
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SUMMARY:HDSI Seminar Series - Xiuyuan Cheng - Wasserstein-regularized learning via neural transport maps: from gradient flow to minimax
DESCRIPTION:Speaker: Xiuyuan Cheng\nDate & Time: Monday February 9th\, 2:00pm\nLocation: HDSI Multipurpose Room 123\n\n\n\nTalk Title: Wasserstein-regularized learning via neural transport maps: from gradient flow to minimax \n\nAbstract: Wasserstein regularization has become a common tool in learning problems over distributions\, while its practical computation remains challenging\, especially in high dimensions. This talk presents a framework for Wasserstein-regularized learning based on directly parameterizing transport maps with neural networks. Rather than working with dual potentials or entropic relaxations\, we explicitly model the transport map\, which enables principled optimization in Wasserstein space as well as scalable out-of-sample evaluation. One example is the implementation of Wasserstein-2 proximal steps via flow networks that realize the Jordan–Kinderlehrer–Otto (JKO) scheme\, yielding a variational interpretation of flow-based generative models. The main focus of the talk is a different regime motivated by distributionally robust optimization (DRO)\, where transport is chosen adversarially through a minimax objective. In this setting\, we establish convergence guarantees for gradient descent–ascent (GDA) dynamics of the Wasserstein minimax problem\, and show how a neural transport map learned from a sample-based matching loss enables direct generation from the worst-case distribution. Together\, these examples highlight both the opportunities and challenges of incorporating Wasserstein regularization into generative modeling\, suggesting that the transport-map formulation offers a flexible and promising way to leverage Wasserstein geometry in learning problems over distributions.\n\nSpeaker Bio: Prof Xiuyuan Cheng currently is Professor of Mathematics at Duke University\, previously as Associate Professor of Mathematics at Trinity College of Arts & Sciences. Prof. Cheng works as an applied analyst\, developing theoretical and computational techniques to solve problems in high-dimensional statistics\, signal processing and machine learning. They are a past recipient of the National Science Foundation CAREER Award as well as the Sloan Research Fellowship-Mathematics.
URL:https://datascience.ucsd.edu/event/hdsi-seminar-series-xiuyuan-cheng/
LOCATION:Halıcıoğlu Data Science Institute (HDSI)\, Room 123\, 3234 Matthews Ln\, La Jolla\, CA\, 92093\, United States
CATEGORIES:Seminar
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