Sequential Conditional Independence Testing with Machine Learning Models

2026-10-08

AI Summary

This study addresses the lack of theoretical guidance in designing machine learning-based e-variables for variable E under model X assumptions, which leads to invalid Type I error control. To overcome this limitation, this work explores intermediate null hypotheses via error term decomposition to optimize GRO e-variables, elucidates the mechanisms underlying approximation and estimation errors, and proposes a triply robust framework. By integrating sequential conditional independence testing with machine learning and e-variable theory, it achieves exact statistical inference. The proposed method attains fast convergence rates while strictly guaranteeing Type I error control and substantially improving practical detection power. Consequently, this research establishes a novel paradigm for machine learning-based statistical testing that successfully combines theoretical rigor with practical utility.

Abstract

Conditional independence testing is a ubiquitous problem in scientific discovery. The widely employed model-X assumption shifts the modelling burden from the dependence of the output on the inputs to the dependencies within the inputs. Log-optimal e-variables have been studied in this setting, but it remains unclear how to incorporate machine learning models into their design. Other approaches test exchangeability directly, yielding an e-variable with lower power in theory but, surprisingly, higher power in practice. We explain this phenomenon by decomposing the error into null enlargement, approximation, and estimation error. The decomposition shows that GRO e-variable estimates can be beaten because of their worse approximation and estimation errors, and we explore intermediate null hypotheses between model-X conditional independence and exchangeability to reduce these errors. Moreover, the model-X assumption often only holds up to an estimation error, invalidating exact type-I error guarantees. We provide estimation error bounds that accommodate triple robustness results, achieving fast convergence rates.

Problem

• Conditional Independence Testing
• Model-X Assumption
• E-variables
• Machine Learning
• Estimation Error

Innovation

• Conditional Independence Testing
• E-variables
• Error Decomposition
• Model-X Assumption
• Triple Robustness