Statistical optimal transport via factored couplings

Aden Forrow, Jan Christian Hütter, Mor Nitzan, Philippe Rigollet, Geoffrey Schiebinger, Jonathan Weed

Research output: Contribution to conferencePaperpeer-review

20 Scopus citations

Abstract

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.

Original languageAmerican English
StatePublished - 2020
Externally publishedYes
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: 16 Apr 201918 Apr 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
Country/TerritoryJapan
CityNaha
Period16/04/1918/04/19

Bibliographical note

Publisher Copyright:
© 2019 by the author(s).

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