Wasserstein Conditional Independence Testing

07/29/2021

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by   Andrew Warren, et al.

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We introduce a test for the conditional independence of random variables X and Y given a random variable Z, specifically by sampling from the joint distribution (X,Y,Z), binning the support of the distribution of Z, and conducting multiple p-Wasserstein two-sample tests. Under a p-Wasserstein Lipschitz assumption on the conditional distributions ℒ_X|Z, ℒ_Y|Z, and ℒ_(X,Y)|Z, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of Z has compact support.