Spotlight
Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
Gonzalo Mena · Jonathan Niles-Weed
We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially on the bound of Genevay et al.~(2019) and extends their work to unbounded measures. Second, we establish a central limit theorem for entropic OT, based on techniques developed by Del Barrio and Loubes~(2019). Previously, such a result was only known for finite metric spaces. As an application of our results, we develop and analyze a new technique for estimating the entropy of a random variable corrupted by gaussian noise.
Author Information
Gonzalo Mena (Harvard)
Jon Niles-Weed (NYU)
Related Events (a corresponding poster, oral, or spotlight)
-
2019 Poster: Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem »
Thu Dec 12th 05:00 -- 07:00 PM Room East Exhibition Hall B + C
More from the Same Authors
-
2019 Poster: Massively scalable Sinkhorn distances via the Nyström method »
Jason Altschuler · Francis Bach · Alessandro Rudi · Jonathan Niles-Weed -
2017 Poster: Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration »
Jason Altschuler · Jonathan Niles-Weed · Philippe Rigollet -
2017 Spotlight: Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration »
Jason Altschuler · Jonathan Niles-Weed · Philippe Rigollet
