Double Generative Adversarial Networks for Conditional Independence Testing

In this article, we study the problem of high-dimensional conditional\nindependence testing, a key building block in statistics and machine learning.\nWe propose an inferential procedure based on double generative adversarial\nnetworks (GANs). Specifically, we first introduce a double GANs framework to\nlearn two generators of the conditional distributions. We then integrate the\ntwo generators to construct a test statistic, which takes the form of the\nmaximum of generalized covariance measures of multiple transformation\nfunctions. We also employ data-splitting and cross-fitting to minimize the\nconditions on the generators to achieve the desired asymptotic properties, and\nemploy multiplier bootstrap to obtain the corresponding $p$-value. We show that\nthe constructed test statistic is doubly robust, and the resulting test both\ncontrols type-I error and has the power approaching one asymptotically. Also\nnotably, we establish those theoretical guarantees under much weaker and\npractically more feasible conditions compared to the existing tests, and our\nproposal gives a concrete example of how to utilize some state-of-the-art deep\nlearning tools, such as GANs, to help address a classical but challenging\nstatistical problem. We demonstrate the efficacy of our test through both\nsimulations and an application to an anti-cancer drug dataset. A Python\nimplementation of the proposed procedure is available at\nhttps://github.com/tianlinxu312/dgcit.\n

Paper

Similar papers

© 2026 NYSGPT2525 LLC