Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

• URL: http://arxiv.org/abs/2606.18993v1
• Date: Wed, 17 Jun 2026 12:16:37 GMT
• Title: Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
• Abstract summary: "Model-X" assumes exact knowledge of a relevant conditional distribution.<n>Existing sequential conditional independence tests require the Model-X conditional to be known exactly.<n>We propose a new approach that is substantially more robust to such estimation error.
• Score: 17.48164930490326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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