Increasing effect sizes of pairwise conditional independence tests between random vectors

Tom Hochsprung, Jonas Wahl, Andreas Gerhardus, Urmi Ninad, Jakob Runge
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:879-889, 2023.

Abstract

A simple approach to test for conditional independence of two random vectors given a third random vector is to simultaneously test for conditional independence of every pair of components of the two random vectors given the third random vector. In this work, we show that conditioning on additional components of the two random vectors that are independent given the third one increases the tests’ effect sizes while leaving the validity of the overall approach unchanged. We leverage this result to derive a practical pairwise testing algorithm that first chooses tests with a relatively large effect size and then does the actual testing. We show both numerically and theoretically that our algorithm outperforms standard pairwise independence testing and other existing methods if the dependence within the two random vectors is sufficiently high.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-hochsprung23a, title = {Increasing effect sizes of pairwise conditional independence tests between random vectors}, author = {Hochsprung, Tom and Wahl, Jonas and Gerhardus, Andreas and Ninad, Urmi and Runge, Jakob}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {879--889}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/hochsprung23a/hochsprung23a.pdf}, url = {https://proceedings.mlr.press/v216/hochsprung23a.html}, abstract = {A simple approach to test for conditional independence of two random vectors given a third random vector is to simultaneously test for conditional independence of every pair of components of the two random vectors given the third random vector. In this work, we show that conditioning on additional components of the two random vectors that are independent given the third one increases the tests’ effect sizes while leaving the validity of the overall approach unchanged. We leverage this result to derive a practical pairwise testing algorithm that first chooses tests with a relatively large effect size and then does the actual testing. We show both numerically and theoretically that our algorithm outperforms standard pairwise independence testing and other existing methods if the dependence within the two random vectors is sufficiently high.} }
Endnote
%0 Conference Paper %T Increasing effect sizes of pairwise conditional independence tests between random vectors %A Tom Hochsprung %A Jonas Wahl %A Andreas Gerhardus %A Urmi Ninad %A Jakob Runge %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-hochsprung23a %I PMLR %P 879--889 %U https://proceedings.mlr.press/v216/hochsprung23a.html %V 216 %X A simple approach to test for conditional independence of two random vectors given a third random vector is to simultaneously test for conditional independence of every pair of components of the two random vectors given the third random vector. In this work, we show that conditioning on additional components of the two random vectors that are independent given the third one increases the tests’ effect sizes while leaving the validity of the overall approach unchanged. We leverage this result to derive a practical pairwise testing algorithm that first chooses tests with a relatively large effect size and then does the actual testing. We show both numerically and theoretically that our algorithm outperforms standard pairwise independence testing and other existing methods if the dependence within the two random vectors is sufficiently high.
APA
Hochsprung, T., Wahl, J., Gerhardus, A., Ninad, U. & Runge, J.. (2023). Increasing effect sizes of pairwise conditional independence tests between random vectors. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:879-889 Available from https://proceedings.mlr.press/v216/hochsprung23a.html.

Related Material