Differentially Private Conditional Independence Testing
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910378815913984 |
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| author | Kalemaj, Iden Kasiviswanathan, Shiva Prasad Ramdas, Aaditya |
| author_facet | Kalemaj, Iden Kasiviswanathan, Shiva Prasad Ramdas, Aaditya |
| contents | 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 Candès 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differentially Private Conditional Independence Testing Kalemaj, Iden Kasiviswanathan, Shiva Prasad Ramdas, Aaditya Machine Learning Cryptography and Security 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 Candès 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. |
| title | Differentially Private Conditional Independence Testing |
| topic | Machine Learning Cryptography and Security |
| url | https://arxiv.org/abs/2306.06721 |