Finding Distributions that Differ, with False Discovery Rate Control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917101696974848 |
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| author | Lee, Yonghoon Dobriban, Edgar Tchetgen, Eric Tchetgen |
| author_facet | Lee, Yonghoon Dobriban, Edgar Tchetgen, Eric Tchetgen |
| contents | We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p-values and demonstrate that they satisfy positive regression dependence across the groups [Benjamini and Yekutieli, 2001], thereby enabling control of the false discovery rate through the Benjamini-Hochberg procedure. The proof of positive regression dependence introduces a novel technique for the inductive construction of rank vectors with almost sure dominance under exchangeability. We evaluate the performance of the proposed procedure through simulations, where, despite being distribution-free, in some cases they show performance comparable to methods with knowledge of the data-generating normal distribution; and further have more power than direct approaches based on conformal out-of-distribution detection. Further, we illustrate our methods on a Hepatitis C treatment dataset, where they can identify patient groups with large treatment effects; and on the Current Population Survey dataset, where they can identify sub-population with long work hours. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_13769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding Distributions that Differ, with False Discovery Rate Control Lee, Yonghoon Dobriban, Edgar Tchetgen, Eric Tchetgen Methodology We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p-values and demonstrate that they satisfy positive regression dependence across the groups [Benjamini and Yekutieli, 2001], thereby enabling control of the false discovery rate through the Benjamini-Hochberg procedure. The proof of positive regression dependence introduces a novel technique for the inductive construction of rank vectors with almost sure dominance under exchangeability. We evaluate the performance of the proposed procedure through simulations, where, despite being distribution-free, in some cases they show performance comparable to methods with knowledge of the data-generating normal distribution; and further have more power than direct approaches based on conformal out-of-distribution detection. Further, we illustrate our methods on a Hepatitis C treatment dataset, where they can identify patient groups with large treatment effects; and on the Current Population Survey dataset, where they can identify sub-population with long work hours. |
| title | Finding Distributions that Differ, with False Discovery Rate Control |
| topic | Methodology |
| url | https://arxiv.org/abs/2505.13769 |