Differentially Private Conditional Independence Testing

Iden Kalemaj, Shiva Kasiviswanathan, Aaditya Ramdas
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3700-3708, 2024.

Abstract

Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand{è}s et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-kalemaj24a, title = {Differentially Private Conditional Independence Testing}, author = {Kalemaj, Iden and Kasiviswanathan, Shiva and Ramdas, Aaditya}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3700--3708}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/kalemaj24a/kalemaj24a.pdf}, url = {https://proceedings.mlr.press/v238/kalemaj24a.html}, abstract = {Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand{è}s et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.} }
Endnote
%0 Conference Paper %T Differentially Private Conditional Independence Testing %A Iden Kalemaj %A Shiva Kasiviswanathan %A Aaditya Ramdas %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-kalemaj24a %I PMLR %P 3700--3708 %U https://proceedings.mlr.press/v238/kalemaj24a.html %V 238 %X Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand{è}s et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.
APA
Kalemaj, I., Kasiviswanathan, S. & Ramdas, A.. (2024). Differentially Private Conditional Independence Testing. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3700-3708 Available from https://proceedings.mlr.press/v238/kalemaj24a.html.

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