In this article, we consider the problem of high-dimensional conditional independence testing, which is a key building block in statistics and machine learning. We propose a double generative adversarial networks (GANs)-based inference procedure. We first introduce a double GANs framework to learn two generators, and integrate the two generators to construct a doubly-robust test statistic. We next consider multiple generalized covariance measures, and take their maximum as our test statistic. Finally, we obtain the empirical distribution of our test statistic through multiplier bootstrap. We show that our test controls type-I error, while the power approaches one asymptotically. More importantly, these theoretical guarantees are obtained under much weaker and practically more feasible conditions compared to existing tests. We demonstrate the efficacy of our test through both synthetic and real datasets.

本文研究高维条件独立性检验问题，在双生成对抗网络（GAN）的基础上提出了一种推理方法，通过多个转换函数的广义协方差度量的最大值来构建测试统计量，并采用数据分割和交叉拟合来实现理论保障条件的最小化。除了控制Type I错误和具有渐近一的能力外，我们的方法使用了倍增样本法，证明了在更弱且更实际可行的条件下比现有测试更可行，并且是如何利用GAN等最先进的深度学习工具来解决传统但具有挑战性的统计问题的一个具体例子。我们通过模拟和一个抗癌药物数据集的应用来展示了我们的测试的有效性。

双生成对抗网络用于条件独立性测试