DeepAI

# An improved central limit theorem and fast convergence rates for entropic transportation costs

We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.

• 18 publications
• 15 publications
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• 28 publications
02/12/2021

### Central Limit Theorems for General Transportation Costs

We consider the problem of optimal transportation with general cost betw...
05/28/2019

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

We prove several fundamental statistical bounds for entropic OT with the...
02/13/2022

### Central Limit Theorems for Semidiscrete Wasserstein Distances

We prove a Central Limit Theorem for the empirical optimal transport cos...
02/21/2022

### Empirical Optimal Transport between Different Measures Adapts to Lower Complexity

The empirical optimal transport (OT) cost between two probability measur...
02/25/2020

### A CLT in Stein's distance for generalized Wishart matrices and higher order tensors

We study the convergence along the central limit theorem for sums of ind...
12/04/2019

### Asymptotics for Strassen's Optimal Transport Problem

In this paper, we consider Strassen's version of optimal transport probl...
06/24/2021

### Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs

We revisit the question of characterizing the convergence rate of plug-i...