Entropic optimal transport is maximum-likelihood deconvolution
Philippe Rigollet, Jonathan Weed · Comptes Rendus Mathématique · 2018
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.