Regression-based conditional independence test with adaptive kernels

We propose a novel framework for regression-based conditional independence (CI) test with adaptive kernels, where the task of CI test is reduced to regression and statistical independence test while proving that the test power of CI can be maximized by adaptively learning parameterized kernels of the independence test if the consistency of regression can be guaranteed. For the adaptively learning kernel of independence test, we first address the pitfall inherent in the existing signal-to-noise ratio criterion by modeling the change of the null distribution during the learning process, then design a new class of kernels that can adaptively focus on the significant dimensions of variables to judge independence, which makes the tests more flexible than using simple kernels that are adaptive only in length-scale, and especially suitable for high-dimensional complex data. Theoretically, we demonstrate the consistency of the proposed tests, and show that the non-convex objective function used for learning fits the L-smoothing condition, thus benefiting the optimization. Experimental results on both synthetic and real data show the superiority of our method. The source code and datasets are available at https://github.com/hzsiat/AdaRCIT.