A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery

TL;DR

This paper introduces a Bayesian nonparametric conditional two-sample test designed for mixed data types, specifically addressing the challenge of testing conditional independence involving binary and continuous variables, crucial for causal discovery.

Contribution

It proposes a novel Bayesian nonparametric test for mixed-type conditional independence, filling a gap in existing methods and enhancing causal discovery algorithms.

Findings

The test performs well on synthetic data.

It outperforms existing methods on real-world datasets.

Improves local causal discovery accuracy.

Abstract

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These algorithms are often applied to datasets containing binary variables, which indicate the 'context' of the observations, e.g. a control or treatment group within an experiment. In these settings, conditional independence testing with $X$ or $Y$ binary (and the other continuous) is paramount to the performance of the causal discovery algorithm. To our knowledge no nonparametric 'mixed' conditional independence test currently exists, and in practice tests that assume all variables to be continuous are used instead. In this paper we aim to fill this gap, as we combine elements of Holmes et al. (2015) and Teymur and Filippi (2020) to propose a novel Bayesian nonparametric conditional two-sample test. Applied to the Local Causal Discovery algorithm, we investigate its performance on both synthetic and real-world data, and compare with state-of-the-art conditional independence tests.