Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Gonzalo Mena, Jonathan Niles-Weed


<p>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.</p>