A Bayesian nonparametric test for conditional independence

TL;DR

This paper presents a Bayesian nonparametric approach using Polya tree priors to test for conditional independence between variables, offering a symmetric measure useful in causal discovery.

Contribution

It introduces a novel Bayesian nonparametric method for assessing conditional independence, incorporating uncertainty in distributional assumptions.

Findings

Provides a symmetric probability measure of dependence and independence

Applicable to causal discovery tasks

Accounts for distributional uncertainty nonparametrically

Abstract

This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of the underlying distributions in a nonparametric way. The Bayesian perspective provides an inherently symmetric probability measure of conditional dependence or independence, a feature particularly advantageous in causal discovery and not employed in existing procedures of this type.