Model-X Sequential Testing for Conditional Independence via Testing by Betting

Shalev Shaer, Gal Maman, Yaniv Romano

Research output: Contribution to journalConference articlepeer-review


This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is conditionally associated with the response under study. We allow the processing of data points online, as soon as they arrive, and stop data acquisition once significant results are detected, rigorously controlling the type-I error rate. Our test can work with any sophisticated machine learning algorithm to enhance data efficiency to the extent possible. The developed method is inspired by two statistical frameworks. The first is the model-X conditional randomization test, a test for conditional independence that is valid in offline settings where the sample size is fixed in advance. The second is testing by betting, a “game-theoretic” approach for sequential hypothesis testing. We conduct synthetic experiments to demonstrate the advantage of our test over out-of-the-box sequential tests that account for the multiplicity of tests in the time horizon, and demonstrate the practicality of our proposal by applying it to real-world tasks.

Original languageEnglish
Pages (from-to)2054-2086
Number of pages33
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain
Duration: 25 Apr 202327 Apr 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


Dive into the research topics of 'Model-X Sequential Testing for Conditional Independence via Testing by Betting'. Together they form a unique fingerprint.

Cite this