Kernel-based Conditional Independence Test and Application in Causal Discovery

Kun Zhang, Jonas Peters, Dominik Janzing, Bernhard Schoelkopf
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:885-894, 2011.

Abstract

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-zhang11b, title = {Kernel-based Conditional Independence Test and Application in Causal Discovery}, author = {Zhang, Kun and Peters, Jonas and Janzing, Dominik and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {885--894}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/zhang11b/zhang11b.pdf}, url = {https://proceedings.mlr.press/r9/zhang11b.html}, abstract = {Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Kernel-based Conditional Independence Test and Application in Causal Discovery %A Kun Zhang %A Jonas Peters %A Dominik Janzing %A Bernhard Schoelkopf %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-zhang11b %I PMLR %P 885--894 %U https://proceedings.mlr.press/r9/zhang11b.html %V R9 %X Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties. %Z Reissued by PMLR on 04 October 2026.
APA
Zhang, K., Peters, J., Janzing, D. & Schoelkopf, B.. (2011). Kernel-based Conditional Independence Test and Application in Causal Discovery. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:885-894 Available from https://proceedings.mlr.press/r9/zhang11b.html. Reissued by PMLR on 04 October 2026.

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