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This paper develops a model-free sequential test for conditionalindependence. The proposed test allows researchers to analyze an incomingi.i.d. data stream with any arbitrary dependency structure, and safely concludewhether a feature is conditionally associated with the response under study. Weallow the processing of data points online, as soon as they arrive, and stopdata acquisition once significant results are detected, rigorously controllingthe type-I error rate. Our test can work with any sophisticated machinelearning algorithm to enhance data efficiency to the extent possible. Thedeveloped method is inspired by two statistical frameworks. The first is themodel-X conditional randomization test, a test for conditional independencethat is valid in offline settings where the sample size is fixed in advance.The second is testing by betting, a ``game-theoretic'' approach for sequentialhypothesis testing. We conduct synthetic experiments to demonstrate theadvantage of our test over out-of-the-box sequential tests that account for themultiplicity of tests in the time horizon, and demonstrate the practicality ofour proposal by applying it to real-world tasks.

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