Adaptive Betting Kernel Test Reduces Type I Error in Conditional Independence

Testing conditional independence is fundamentally difficult – without strong assumptions, Type I error control is impossible in general. The 'Model-X' paradigm circumvents this by assuming exact knowledge of a relevant conditional distribution. However, existing sequential conditional independence tests require this distribution to be known exactly, making them fragile when it must be estimated from data. Zheng He and Danica J. Sutherland from the University of British Columbia (published at ICML 2026) introduce a novel approach that is substantially more robust to such estimation error, using a testing-by-betting framework with an adaptively optimized Kernel Conditional Independence (KCI) statistic.

Their method incorporates a carefully designed normalization scheme and a truncate-and-shift calibration strategy that greatly reduces Type I error inflation while preserving high statistical power. On high-dimensional synthetic benchmarks and real-world fairness tasks, the approach consistently outperforms existing sequential Model-X methods, demonstrating practical viability for applications where the true conditional distribution is unknown. The authors have released code on GitHub, enabling researchers to apply this robust test in causal discovery, algorithmic fairness auditing, and other scenarios requiring reliable sequential conditional independence testing.