A Permutation-Based Kernel Conditional Independence Test

Gary Doran Case Western Reserve University, Krikamol Muandet MPI for Intelligent Systems, Kun Zhang MPI for Intelligent Systems, Bernhard Schölkopf
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:116-125, 2014.

Abstract

Determining conditional independence (CI) relationships between random variables is a challenging but important task for problems such as Bayesian network learning and causal discovery. We propose a new kernel CI test that uses a single, learned permutation to convert the CI test problem into an easier two-sample test problem. The learned permutation leaves the joint distribution unchanged if and only if the null hypothesis of CI holds. Then, a kernel two-sample test, which has been studied extensively in prior work, can be applied to a permuted and an unpermuted sample to test for CI. We demonstrate that the test (1) easily allows the incorporation of prior knowledge during the permutation step, (2) has power competitive with state-of-the-art kernel CI tests, and (3) accurately estimates the null distribution of the test statistic, even as the dimensionality of the conditioning variable grows.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-university14c, title = {A Permutation-Based Kernel Conditional Independence Test}, author = {University, Gary Doran Case Western Reserve and Systems, Krikamol Muandet MPI for Intelligent and Systems, Kun Zhang MPI for Intelligent and Sch{\"o}lkopf, Bernhard}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {116--125}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/university14c/university14c.pdf}, url = {https://proceedings.mlr.press/r12/university14c.html}, abstract = {Determining conditional independence (CI) relationships between random variables is a challenging but important task for problems such as Bayesian network learning and causal discovery. We propose a new kernel CI test that uses a single, learned permutation to convert the CI test problem into an easier two-sample test problem. The learned permutation leaves the joint distribution unchanged if and only if the null hypothesis of CI holds. Then, a kernel two-sample test, which has been studied extensively in prior work, can be applied to a permuted and an unpermuted sample to test for CI. We demonstrate that the test (1) easily allows the incorporation of prior knowledge during the permutation step, (2) has power competitive with state-of-the-art kernel CI tests, and (3) accurately estimates the null distribution of the test statistic, even as the dimensionality of the conditioning variable grows.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Permutation-Based Kernel Conditional Independence Test %A Gary Doran Case Western Reserve University %A Krikamol Muandet MPI for Intelligent Systems %A Kun Zhang MPI for Intelligent Systems %A Bernhard Schölkopf %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-university14c %I PMLR %P 116--125 %U https://proceedings.mlr.press/r12/university14c.html %V R12 %X Determining conditional independence (CI) relationships between random variables is a challenging but important task for problems such as Bayesian network learning and causal discovery. We propose a new kernel CI test that uses a single, learned permutation to convert the CI test problem into an easier two-sample test problem. The learned permutation leaves the joint distribution unchanged if and only if the null hypothesis of CI holds. Then, a kernel two-sample test, which has been studied extensively in prior work, can be applied to a permuted and an unpermuted sample to test for CI. We demonstrate that the test (1) easily allows the incorporation of prior knowledge during the permutation step, (2) has power competitive with state-of-the-art kernel CI tests, and (3) accurately estimates the null distribution of the test statistic, even as the dimensionality of the conditioning variable grows. %Z Reissued by PMLR on 04 October 2026.
APA
University, G.D.C.W.R., Systems, K.M.M.f.I., Systems, K.Z.M.f.I. & Schölkopf, B.. (2014). A Permutation-Based Kernel Conditional Independence Test. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:116-125 Available from https://proceedings.mlr.press/r12/university14c.html. Reissued by PMLR on 04 October 2026.

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