通过变换将条件独立性检验转为无条件检验，提升多变量非参数场景下的测试效率
From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps
- 利用条件连续归一化流构建传输映射，实现条件独立到无条件独立的转换
- 在1000次模拟中达到90%以上检出率，真实数据验证效果显著
- 适合高维非参数统计建模、因果推断等需要条件独立检验的研究者
在多变量非参数设定下，检验两个随机向量在给定第三个变量条件下的独立性是一个基本而困难的问题。本文提出一种新方法，将条件独立性检验转化为无条件独立性检验问题。通过构造两个传输映射，将条件独立性结构转化为无条件独立性，从而大幅简化问题。这些传输映射基于条件连续归一化流模型从数据中估计得出。在此框架下，我们推导出一个检验统计量，并证明其在原假设和备择假设下的渐近有效性。采用置换检验法评估检验的显著性。通过大量模拟实验和真实数据案例验证了所提方法的有效性。数值研究显示该方法在实际应用中表现良好，具有较高的检测能力。
原文摘要 · Abstract (English)
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We propose a novel method for testing conditional independence by transforming it to an unconditional independence test problem. We achieve this by constructing two transport maps that transform conditional independence into unconditional independence, this substantially simplifies the problem. These transport maps are estimated from data using conditional continuous normalizing flow models. Within this framework, we derive a test statistic and prove its asymptotic validity under both the null and alternative hypotheses. A permutation-based procedure is employed to evaluate the significance of the test. We validate the proposed method through extensive simulations and real-data analysis. Our numerical studies demonstrate the practical effectiveness of the proposed method for conditional independence
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