Practical Kernel Tests of Conditional Independence
This work addresses a statistical testing problem for researchers and practitioners in machine learning and statistics, offering an incremental improvement to existing methods.
The paper tackles the challenge of controlling false positives in kernel-based conditional independence tests while maintaining competitive power, proposing SplitKCI, which significantly improves test level control without sacrificing power, as demonstrated theoretically and on synthetic and real-world data.
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.