论文标题
通过投注通过测试进行有条件独立性的模型-X顺序测试
Model-X Sequential Testing for Conditional Independence via Testing by Betting
论文作者
论文摘要
本文为条件独立性开发了无模型的顺序测试。提出的测试允许研究人员分析传入的I.I.D.具有任何任意依赖性结构的数据流，并安全地得出一个特征是否与所研究的响应有条件地相关联。我们允许数据点到达后立即在线处理，并在检测到重大结果后停止数据采集，严格控制I型错误率。我们的测试可以与任何复杂的机器学习算法一起使用，以提高数据效率。开发的方法灵感来自两个统计框架。第一个是Model-X条件随机测试，该测试是针对有条件独立性的测试，该测试在样本大小预先固定的离线设置中有效。第二个是通过投注进行测试，这是一种顺序假设检验的``游戏理论''方法。我们进行综合实验，以证明我们的测试优于定期的顺序测试，这些测试占时间范围内的多个测试，并通过将其应用于现实世界任务来证明我们的建议的实用性。
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.
