Conditional Independence Testing using Generative Adversarial Networks

TL;DR

This paper introduces a novel conditional independence test leveraging GANs to directly approximate conditional distributions, achieving higher power in high-dimensional settings without distributional assumptions.

Contribution

The authors propose a GAN-based test statistic for conditional independence that controls false positives and improves detection power in high-dimensional data.

Findings

Significant power gains over existing methods in synthetic high-dimensional data

Effective identification of causal disease markers in genetic data

No assumptions on distribution forms or dependencies required

Abstract

We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to approximate directly a conditional distribution that encodes the null hypothesis, in a manner that maximizes power (the rate of true negatives). We show that such an approach requires only that density approximation be viable in order to ensure that we control type I error (the rate of false positives); in particular, no assumptions need to be made on the form of the distributions or feature dependencies. Using synthetic simulations with high-dimensional data we demonstrate significant gains in power over competing methods. In addition, we illustrate the use of our test to discover causal markers of disease in genetic data.