Entropic optimal transport is maximum-likelihood deconvolution

TL;DR

This paper reveals that entropic optimal transport can be understood as maximum-likelihood deconvolution for Gaussian models, providing a theoretical foundation for its widespread use in machine learning.

Contribution

It establishes a statistical interpretation of entropic optimal transport as maximum-likelihood estimation in Gaussian deconvolution, linking optimal transport to statistical inference.

Findings

Entropic optimal transport corresponds to maximum-likelihood Gaussian deconvolution.

Provides theoretical justification for using entropic OT in machine learning.

Links optimal transport projections to statistical estimation methods.

Abstract

We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.