A Kernel-Based Test for Multi-Way Conditional Independence
Abstract
Conditional independence involving more than two variables, or multi-way conditional independence, is a fundamental probabilistic structure useful in many areas of statistical research, including latent-variable and graphical models. However, most existing works focus on pairwise conditional independence. To address this gap, we propose a kernel-based test of multi-way conditional independence. Specifically, we characterize this hypothesis through the simultaneous vanishing of a vector of conditional cross-covariance operators and construct a test statistic based on the norm of the vector of their estimators. We derive the statistic's asymptotic distributions under the null hypothesis and local alternatives. As a related methodological contribution, we also develop a test of multi-way unconditional independence and provide a procedure for its implementation. An application to RNA data illustrates the method's use in genomics.
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BibTeX
@misc{chen2026kernelbased,
title = {{A Kernel-Based Test for Multi-Way Conditional Independence}},
author = {Haoning Chen and Yin Tang and Bing Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01092},
eprint = {2611.01092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01092},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Kernel-Based Test for Multi-Way Conditional Independence
AU - Haoning Chen
AU - Yin Tang
AU - Bing Li
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01092
UR - https://arxiv.org/abs/2611.01092
AB - Conditional independence involving more than two variables, or multi-way conditional independence, is a fundamental probabilistic structure useful in many areas of statistical research, including latent-variable and graphical models. However, most existing works focus on pairwise conditional independence. To address this gap, we propose a kernel-based test of multi-way conditional independence. Specifically, we characterize this hypothesis through the simultaneous vanishing of a vector of conditional cross-covariance operators and construct a test statistic based on the norm of the vector of their estimators. We derive the statistic's asymptotic distributions under the null hypothesis and local alternatives. As a related methodological contribution, we also develop a test of multi-way unconditional independence and provide a procedure for its implementation. An application to RNA data illustrates the method's use in genomics.
ER -