A conditional independence test generates null samples via sliced score matching and Langevin dynamics, adds a goodness-of-fit check, and gives an asymptotic Type I error bound.
Wasserstein Conditional Independence Testing
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abstract
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 $\mathcal{L}_{X|Z}$, $\mathcal{L}_{Y|Z}$, and $\mathcal{L}_{(X,Y)|Z}$, 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.
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Score-based Generative Modeling for Conditional Independence Testing
A conditional independence test generates null samples via sliced score matching and Langevin dynamics, adds a goodness-of-fit check, and gives an asymptotic Type I error bound.