Kernel-based Conditional Independence Test and Application in Causal Discovery

TL;DR

This paper introduces a kernel-based method for conditional independence testing that is computationally efficient and effective in high-dimensional settings, aiding causal discovery and Bayesian network learning.

Contribution

The paper proposes the KCI-test, a novel kernel-based approach for conditional independence testing with an asymptotic distribution derivation, improving performance in high-dimensional data.

Findings

Outperforms existing methods in large conditioning sets

Effective with small to moderate sample sizes

Computationally efficient and easy to implement

Abstract

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.