Seminar: Optimal transport methods in statistics and machine learning: theory and applications

SpeakerQuentin Berthet
AffiliationUniversity of Cambridge
DateThursday, 30 May 2019
Time13:00 - 14:00
LocationRoberts 106
Event seriesDeepMind CSML Seminar Series
Description

Optimal transport is one of the foundational problems of optimization, and a very important topic in analysis. It asks how one can transport mass with a given measure to have another measure, with minimal global transport cost. The associated Wasserstein distance is a useful tool to compare distributions, taking into account geometric properties of the data.
In this presentation, I will talk about two recent projects on this topic. In the first one, we propose a novel approach for unsupervised embedding alignment, and show applications to natural language processing. It is based on a new approach for Wasserstein loss minimization (joint work with E. Grave and A. Joulin, AISTATS 2019). In the second one, we provide new methods and guarantees for estimation of distributions with smooth densities, in Wasserstein distance. We show that these tools, inspired by techniques in nonparametric statistics, yield information-theoretic optimal results. We also develop ideas to handle our proposed estimators in a computationally efficient manner, and explore some of the associated computational trade-offs (joint work with J. Weed, COLT 2019).

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