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

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 languageEnglish (US)
StatePublished - 2020
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
CountryJapan
CityNaha
Period4/16/194/18/19

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

Fingerprint Dive into the research topics of 'Statistical optimal transport via factored couplings'. Together they form a unique fingerprint.

Cite this