A Kernel Test for Three-Variable Interactions with Random Processes

Paul Rubenstein, Kacper Chwialkowski UCL / Gatsby Unit, Arthur Gretton Gatsby Unit
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:692-701, 2016.

Abstract

We apply a wild bootstrap method to the Lancaster three-variable interaction measure in order to detect factorisation of the joint distribution on three variables forming a stationary random process, for which the existing permutation bootstrap method fails. As in the i.i.d. case, the Lancaster test is found to outperform existing tests in cases for which two independent variables individually have a weak influence on a third, but that when considered jointly the influence is strong. The main contributions of this paper are twofold: first, we prove that the Lancaster statistic satisfies the conditions required to estimate the quantiles of the null distribution using the wild bootstrap; second, the manner in which this is proved is novel, simpler than existing methods, and can further be applied to other statistics.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-rubenstein16a, title = {A Kernel Test for Three-Variable Interactions with Random Processes}, author = {Rubenstein, Paul and Unit, Kacper Chwialkowski UCL / Gatsby and Unit, Arthur Gretton Gatsby}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {692--701}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/rubenstein16a/rubenstein16a.pdf}, url = {https://proceedings.mlr.press/r14/rubenstein16a.html}, abstract = {We apply a wild bootstrap method to the Lancaster three-variable interaction measure in order to detect factorisation of the joint distribution on three variables forming a stationary random process, for which the existing permutation bootstrap method fails. As in the i.i.d. case, the Lancaster test is found to outperform existing tests in cases for which two independent variables individually have a weak influence on a third, but that when considered jointly the influence is strong. The main contributions of this paper are twofold: first, we prove that the Lancaster statistic satisfies the conditions required to estimate the quantiles of the null distribution using the wild bootstrap; second, the manner in which this is proved is novel, simpler than existing methods, and can further be applied to other statistics.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Kernel Test for Three-Variable Interactions with Random Processes %A Paul Rubenstein %A Kacper Chwialkowski UCL / Gatsby Unit %A Arthur Gretton Gatsby Unit %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-rubenstein16a %I PMLR %P 692--701 %U https://proceedings.mlr.press/r14/rubenstein16a.html %V R14 %X We apply a wild bootstrap method to the Lancaster three-variable interaction measure in order to detect factorisation of the joint distribution on three variables forming a stationary random process, for which the existing permutation bootstrap method fails. As in the i.i.d. case, the Lancaster test is found to outperform existing tests in cases for which two independent variables individually have a weak influence on a third, but that when considered jointly the influence is strong. The main contributions of this paper are twofold: first, we prove that the Lancaster statistic satisfies the conditions required to estimate the quantiles of the null distribution using the wild bootstrap; second, the manner in which this is proved is novel, simpler than existing methods, and can further be applied to other statistics. %Z Reissued by PMLR on 04 October 2026.
APA
Rubenstein, P., Unit, K.C.U./.G. & Unit, A.G.G.. (2016). A Kernel Test for Three-Variable Interactions with Random Processes. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:692-701 Available from https://proceedings.mlr.press/r14/rubenstein16a.html. Reissued by PMLR on 04 October 2026.

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