TY - JOUR

T1 - DIET

T2 - 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023

AU - Sudarshan, Mukund

AU - Puli, Aahlad

AU - Tansey, Wesley

AU - Ranganath, Rajesh

N1 - Funding Information:
We thank the reviewers for their thoughtful comments. We would like to thank the participants of the Selective Inference Seminar for their helpful feedback: in particular Lihua Lei, Rina Barber, and Lucas Janson. This work was supported by the PhRMA Foundation Predoctoral Fellowship, NIH/NHLBI Award R01HL148248, NSF Award 1922658 NRT-HDR: FUTURE Foundations, Translation, and Responsibility for Data Science, NSF CAREER Award 2145542, NIH U54CA274492, R37CA271186, Break Through Cancer, and the Tow Center for Developmental Oncology.
Publisher Copyright:
Copyright © 2023 by the author(s)

PY - 2023

Y1 - 2023

N2 - Conditional randomization tests (CRTs) assess whether a variable x is predictive of another variable y, having observed covariates z. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: Fx|z(x | z) and Fy|z(y | z) where F·|z(· | z) is a conditional cumulative distribution function (CDF) for the distribution p(· | z). These variables are termed “information residuals.” We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.

AB - Conditional randomization tests (CRTs) assess whether a variable x is predictive of another variable y, having observed covariates z. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: Fx|z(x | z) and Fy|z(y | z) where F·|z(· | z) is a conditional cumulative distribution function (CDF) for the distribution p(· | z). These variables are termed “information residuals.” We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.

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M3 - Conference article

AN - SCOPUS:85165175389

SN - 2640-3498

VL - 206

SP - 10343

EP - 10367

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

Y2 - 25 April 2023 through 27 April 2023

ER -