Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
Gonzalo Mena, Jonathan Niles-Weed
Abstract
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.
BibTeX
@inproceedings{NEURIPS2019_5acdc9ca,
author = {Mena, Gonzalo and Niles-Weed, Jonathan},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/5acdc9ca5d99ae66afdfe1eea0e3b26b-Paper.pdf},
volume = {32},
year = {2019}
}