Transport Dependency: Optimal Transport Based Dependency Measures

Understand

Finding meaningful ways to measure the statistical dependency between random variables $\xi$ and $\zeta$ is a timeless statistical endeavor.

• In recent years, several novel concepts, like the distance covariance, have extended classical notions of dependency to more general settings.
• In this article, we propose and study an alternative framework that is based on optimal transport.
• The transport dependency $\tau \ge 0$ applies to general Polish spaces and intrinsically respects metric properties.