Entropy Regularized Optimal Transport Independence Criterion
This provides a new statistical tool for independence testing with applications in synthetic and real data analysis.
The authors tackled the problem of testing independence between two samples by introducing a new criterion based on entropy regularized optimal transport, establishing non-asymptotic bounds and demonstrating its ability to capture linear and nonlinear dependencies in experiments.
We introduce 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 hypothesis and the alternative hypothesis. The theoretical results involve tools from U-process theory and optimal transport theory. We also offer a random feature type approximation for large-scale problems, as well as a differentiable program implementation for deep learning applications. We present experimental results on existing benchmarks for independence testing, illustrating the interest of the proposed criterion to capture both linear and nonlinear dependencies in synthetic data and real data.