BIRS Workshop Lecture Videos
New numerical tools for optimal transport and their machine learning applications Ye, Jianbo
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.
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