Toward Scalable and Valid Conditional Independence Testing with Spectral Representations

Alek Fröhlich, Vladimir R Kostic, Karim Lounici, Daniel Perazzo, Daniel Guimarães Tiezzi, Massimiliano Pontil
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:31669-31702, 2026.

Abstract

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity and scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-frohlich26a, title = {Toward Scalable and Valid Conditional Independence Testing with Spectral Representations}, author = {Fr\"{o}hlich, Alek and Kostic, Vladimir R and Lounici, Karim and Perazzo, Daniel and Tiezzi, Daniel Guimar\~{a}es and Pontil, Massimiliano}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {31669--31702}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/frohlich26a/frohlich26a.pdf}, url = {https://proceedings.mlr.press/v306/frohlich26a.html}, abstract = {Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity and scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.} }
Endnote
%0 Conference Paper %T Toward Scalable and Valid Conditional Independence Testing with Spectral Representations %A Alek Fröhlich %A Vladimir R Kostic %A Karim Lounici %A Daniel Perazzo %A Daniel Guimarães Tiezzi %A Massimiliano Pontil %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-frohlich26a %I PMLR %P 31669--31702 %U https://proceedings.mlr.press/v306/frohlich26a.html %V 306 %X Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity and scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.
APA
Fröhlich, A., Kostic, V.R., Lounici, K., Perazzo, D., Tiezzi, D.G. & Pontil, M.. (2026). Toward Scalable and Valid Conditional Independence Testing with Spectral Representations. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:31669-31702 Available from https://proceedings.mlr.press/v306/frohlich26a.html.

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