Sudarshan Mukund, Puli Aahlad, Tansey Wesley, Ranganath Rajesh
Computer Science, New York University.
Computational Oncology Memorial Sloan Kettering Cancer Center.
Proc Mach Learn Res. 2023 Apr;206:10343-10367.
Conditional randomization tests (CRTs) assess whether a variable is predictive of another variable , having observed covariates . CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: and where is a conditional cumulative distribution function (CDF) for the distribution . These variables are termed "information residuals." We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.
条件随机化检验（CRTs）在观测到协变量的情况下，评估一个变量是否能预测另一个变量。CRTs需要拟合大量的预测模型，这在计算上通常难以处理。现有的降低CRTs成本的解决方案通常将数据集拆分为训练集和测试集，或者依赖启发式方法处理交互作用，这两种方法都会导致检验效能的损失。我们提出了解耦独立性检验（DIET），这是一种算法，通过利用边际独立性统计量来检验条件独立性关系，从而避免了上述两个问题。DIET检验两个随机变量的边际独立性： 和 ，其中 是分布 的条件累积分布函数（CDF）。这些变量被称为“信息残差”。我们给出了DIET实现有限样本类型1错误控制和检验效能大于类型1错误率的充分条件。然后我们证明，当使用信息残差之间的互信息作为检验统计量时，DIET产生最有效的条件有效检验。最后，我们表明DIET在几个合成和真实基准上比其他可处理的CRTs具有更高的检验效能。
