Neural Information Processing Systems http://nips.cc/

The paper is outlined as follows.

We thank all reviewers for their thorough assessment of our paper . This ensures the resulting test produces "well-behaved" We will discuss this further in the revised manuscript, thank you for raising this point. However, insights can also be derived by considering the bound in Theorem 1. Theorem 1 shows that In practice, good performance may also be achieved using other flexible generative models. On the quality of generated samples and stability of p-values - Please kindly refer to the response to Reviewer #3.

Originality This paper presents a new way to use GANs in hypothesis testing. It was very interesting to use GANs to construct a null distribution that adapts to the dataset without strong assumptions. The proposed method can be used for feature selection and explainable neural networks. The quantitative experimental results are limited to synthetic data but comprehensive and expected behaviours of the GCIT are observed in synthetic experiments. The only experimental result with real data is shown but it is hard to tell which result is more accurate and powerful.

We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to approximate directly a conditional distribution that encodes the null hypothesis, in a manner that maximizes power (the rate of true negatives). We show that such an approach requires only that density approximation be viable in order to ensure that we control type I error (the rate of false positives); in particular, no assumptions need to be made on the form of the distributions or feature dependencies. Using synthetic simulations with high-dimensional data we demonstrate significant gains in power over competing methods. In addition, we illustrate the use of our test to discover causal markers of disease in genetic data.