# Model-Free Sequential Testing for Conditional Independence via Testing by Betting

**Authors:** Shalev Shaer, Gal Maman, Yaniv Romano  
**arXiv:** [2210.00354](https://arxiv.org/abs/2210.00354)  
**Date:** 2022-10-01  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2210.00354v1/

## Key points

- Authors Shalev Shaer, Gal Maman, and Yaniv Romano introduce a novel model-free sequential test for analyzing conditional independence in data streams
- The test enables researchers to determine if a feature is conditionally associated with the response by processing incoming data points online and halting data acquisition upon detecting significant results
- Maintains strict control over the type-I error rate
- Can be seamlessly integrated with sophisticated machine learning algorithms, enhancing data efficiency
- Inspired by model-X conditional randomization test and testing by betting frameworks
- Demonstrated effectiveness through synthetic experiments, showing superiority in accuracy and practicality compared to traditional sequential tests
- Applied to real-world tasks, highlighting potential impact on various research domains

## Summary

In their paper titled "Model-Free Sequential Testing for Conditional Independence via Testing by Betting," authors Shalev Shaer, Gal Maman, and Yaniv Romano introduce a novel model-free sequential test for analyzing conditional independence in data streams with varying dependency structures. This innovative test enables researchers to determine whether a feature is conditionally associated with the response under study by processing incoming data points online and halting data acquisition upon detecting significant results. It also maintains strict control over the type-I error rate. The flexibility of this test allows it to be seamlessly integrated with sophisticated machine learning algorithms, enhancing data efficiency. Drawing inspiration from two statistical frameworks - the model-X conditional randomization test and testing by betting - the authors demonstrate the effectiveness of their approach through synthetic experiments. They compare their method to traditional sequential tests that consider multiple tests within a time horizon and showcase its superiority in terms of accuracy and practicality. Additionally, they apply their proposed test to real-world tasks, highlighting its potential impact on various research domains. Overall, this paper presents a cutting-edge solution for conducting sequential hypothesis testing in dynamic data environments and offers a valuable tool for efficiently exploring conditional associations.