Open Collections

New numerical tools for optimal transport and their machine learning applications

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, I plan to introduce my recent work on two numerical tools that solve optimal transport and its related problems. The first tool is a Bregman ADMM approach to solve optimal transport and Wasserstein barycenter. Based on my empirical experience, I will discuss its pro and cons in practice, and compare it with the popular entropic regularization approach. The second tool is a simulated annealing approach to solve Wasserstein minimization problems, in which I will illustrate there exists a simple Markov chain underpinning the dual OT. This approach gives very different approximate solution compared to other smoothing techniques. I will also discuss how this approach will be related to solve some more recent problems in machine learning, such as Wasserstein NMF, out-of-sample mapping estimation. Finally, I will present several applications in document analysis, sequence modeling, and image analytics, using those tools which I have developed during my PhD research.

Mathematics; Calculus of variations and optimal control; optimization; Statistics; Scientific computing

video/mp4

Author affiliation: Penn State University

2017-11-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63507

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/