Practical Kernel Tests of Conditional Independence

TL;DR

This paper introduces SplitKCI, a data-efficient, kernel-based method for conditional independence testing that effectively controls false positives and maintains test power through bias correction via data splitting.

Contribution

The paper presents a novel bias correction technique for kernel-based conditional independence tests using data splitting, improving test accuracy and reliability.

Findings

SplitKCI improves test level control in conditional independence testing.

The method maintains high test power while reducing false positives.

Validated on synthetic and real-world datasets.

Abstract

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of false positives), while still attaining competitive test power. Excess false positives arise due to bias in the test statistic, which is in our case obtained using nonparametric kernel ridge regression. We propose SplitKCI, an automated method for bias control for the Kernel-based Conditional Independence (KCI) test based on data splitting. We show that our approach significantly improves test level control for KCI without sacrificing test power, both theoretically and for synthetic and real-world data.