Increasing Effect Sizes of Pairwise Conditional Independence Tests between Random Vectors

Tom Hochsprung, Jonas Wahl, Andreas Gerhardus, Urmi Ninad, Jakob Runge

Keywords: conditional independence, effect size, non-parametric test, statistics

TL;DR: Our paper introduces a new pairwise conditional independence testing algorithm.

Abstract:

A simple approach to test for conditional independence of two random vectors given a third random vector is to simultaneously test for conditional independence of every pair of components of the two random vectors given the third random vector. In this work, we show that conditioning on additional components of the two random vectors that are independent given the third one increases the tests' effect sizes while leaving the validity of the overall approach unchanged. Up to the effective reduction of the sample size due to enlarging the conditioning sets, these larger effect sizes lead to higher statistical power.
We leverage this result to derive a practical pairwise testing algorithm that first chooses tests with a relatively large effect size and then does the actual testing. In simulations, our algorithm outperforms standard pairwise independence testing and other existing methods if the dependence within the two random vectors is sufficiently high.