Entropy Regularized Optimal Transport Independence Criterion

Optimal transport (OT) and its entropy regularized offspring have recently gained a lot of attention in both machine learning and AI domains. In particular, optimal transport has been used to develop probability metrics between probability distributions. We introduce in this paper an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic, and study its statistical behavior under both the null and alternative hypothesis. Our theoretical results involve tools from U-process theory and optimal transport theory. We present experimental results on existing benchmarks, illustrating the interest of the proposed criterion.