Practical Kernel Learning for Kernel-based Conditional Independent Test

Wenjie Wang, Mingming Gong, Biwei Huang, James Bailey, Bo Han, Kun Zhang, Feng Liu

Keywords: kernel selection, conditional independence, hypothesis testing

Abstract: Conditional independence (CI) test stands as a fundamental and challenging task within modern statistics and machine learning. One pivotal class of methods for assessing conditional independence encompasses kernel-based approaches, known for their capability to identify general conditional dependence without necessitating assumptions about the conditional relationship or resorting to the simulation of intricate conditional distributions. As with any method utilizing kernels, selecting the appropriate kernel in kernel-based CI methods is critical for ensuring heightened test power and precise identification of conditional relationship. However, current methods typically involve the manual heuristic selection of kernel parameters, neglecting the inherent characteristics of the data and potentially leading to errors. In this paper, we propose a kernel parameter selection approach for the Kernel-based Conditional Independence test method (KCI). We decompose the statistic of KCI and treat the kernel applied on the conditioning set as a trainable component. The kernel parameters involved are then learned by maximizing the ratio of the estimated statistic to its variance, which approximates the test power at large sample sizes. Therefore, our method can learn the kernel parameters with increased test power at a very small additional computation cost. Extensive experiments demonstrate the effectiveness of our proposed approach in conditional independence testing and its enhancements to constrain-based causal discovery.

Primary Area: causal reasoning

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Submission Number: 5524