Wasserstein Conditional Independence Testing
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929231185838080 |
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| author | Warren, Andrew |
| author_facet | Warren, Andrew |
| contents | We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting multiple $p$-Wasserstein two-sample tests. Under a $p$-Wasserstein Lipschitz assumption on the conditional distributions $\mathcal{L}_{X|Z}$, $\mathcal{L}_{Y|Z}$, and $\mathcal{L}_{(X,Y)|Z}$, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of $Z$ has compact support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_14184 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Wasserstein Conditional Independence Testing Warren, Andrew Statistics Theory Optimization and Control 62G10 (Primary), 49Q22 (Secondary) We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting multiple $p$-Wasserstein two-sample tests. Under a $p$-Wasserstein Lipschitz assumption on the conditional distributions $\mathcal{L}_{X|Z}$, $\mathcal{L}_{Y|Z}$, and $\mathcal{L}_{(X,Y)|Z}$, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of $Z$ has compact support. |
| title | Wasserstein Conditional Independence Testing |
| topic | Statistics Theory Optimization and Control 62G10 (Primary), 49Q22 (Secondary) |
| url | https://arxiv.org/abs/2107.14184 |