Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

2026-06-17

AI Summary

This work addresses the vulnerability of sequential conditional independence tests to model misspecification when estimating conditional distributions, which can lead to inflated Type I error rates. To overcome this limitation, the authors propose a robust sequential Model-X testing procedure that integrates an adaptively optimized kernel-based conditional independence statistic within the test-if-bet framework. The method incorporates normalization, truncation, and shift calibration mechanisms to effectively mitigate bias arising from estimation errors in the conditional distribution. Both theoretical analysis and empirical evaluations demonstrate that the proposed approach rigorously controls Type I error even in the presence of such estimation inaccuracies, while achieving substantially higher statistical power than existing methods. Its superior performance is consistently observed across high-dimensional synthetic benchmarks and real-world fairness-aware tasks, highlighting its robustness and efficacy.

Abstract

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.

Problem

• conditional independence testing
• Model-X
• sequential testing
• Type I error control
• distribution estimation

Innovation

• sequential testing
• conditional independence
• testing-by-betting
• kernel methods
• Model-X