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

TL;DR

This paper introduces a model-free, sequential testing method for conditional independence that processes data online, controls error rates, and integrates machine learning to improve data efficiency, applicable in real-time data analysis.

Contribution

It develops a novel sequential test combining model-X conditional randomization and testing by betting, enabling real-time, error-controlled conditional independence testing with machine learning integration.

Findings

Outperforms traditional sequential tests in synthetic experiments.

Demonstrates practical application on real-world data.

Effectively controls type-I error in online settings.

Abstract

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.