DIET: Conditional independence testing with marginal dependence measures of residual information
DIET: Conditional independence testing with marginal dependence measures of residual information
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DOI：
10.48550/arxiv.2208.08579
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发表时间：
2022-08
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影响因子：
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通讯作者：
Mukund Sudarshan;A. Puli;Wesley Tansey;R. Ranganath
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作者：
Mukund Sudarshan;A. Puli;Wesley Tansey;R. Ranganath
条件随机化检验（CRT）评估变量x是否预测另一个变量y，观察协变量z。CRT需要拟合大量的预测模型，这通常在计算上是难以处理的。现有的降低CRT成本的解决方案通常将数据集分为训练和测试部分，或者依赖于交互的并行计算，这两者都会导致功率损失。我们提出了解耦独立性测试（DIET），利用边际独立统计来测试条件独立关系，从而避免了这两个问题的算法。DIET测试两个随机变量的边际独立性：Fx z（x z）和Fy z（y z），其中F z（x z）是分布p（x z）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错误控制和大于类型1错误率的功率的充分条件。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产生最强大的条件有效检验。最后，我们显示DIET实现了更高的功率比其他易处理的CRT在几个合成和真实的基准。
Conditional randomization tests (CRTs) assess whether a variable x is predictive of another variable y, having observed covariates z. 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: Fx∣z(x∣z) and Fy∣z(y∣z) where F⋅∣z(⋅∣z) is a conditional cumulative distribution function (CDF) for the distribution p(⋅∣z). 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.