Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.29388 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913177536561152 |
|---|---|
| author | Kuang, Qi Gang, Bowen Xia, Yin |
| author_facet | Kuang, Qi Gang, Bowen Xia, Yin |
| contents | This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($μ$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian distribution. Using this distribution, we derive a globally sharp rejection threshold that strictly improves upon the standard Markov bound. Asymptotic analysis shows that in low-sensitivity regimes, the calibrated private test achieves a net power gain over the non-private baseline. For multiple testing, we introduce a recursive peeling algorithm that adaptively concentrates the privacy budget on the most promising hypotheses. This construction guarantees rigorous $μ$-GDP and yields valid private $e$-values compatible with standard multiple testing procedures. Simulations and a genome-wide association study confirm that the method controls the false discovery rate while improving upon naive all-noisy privatization and recovering power close to non-private benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian Differentially Private $e$-values: Construction, Threshold Calibration, and Multiple Testing Kuang, Qi Gang, Bowen Xia, Yin Methodology This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($μ$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian distribution. Using this distribution, we derive a globally sharp rejection threshold that strictly improves upon the standard Markov bound. Asymptotic analysis shows that in low-sensitivity regimes, the calibrated private test achieves a net power gain over the non-private baseline. For multiple testing, we introduce a recursive peeling algorithm that adaptively concentrates the privacy budget on the most promising hypotheses. This construction guarantees rigorous $μ$-GDP and yields valid private $e$-values compatible with standard multiple testing procedures. Simulations and a genome-wide association study confirm that the method controls the false discovery rate while improving upon naive all-noisy privatization and recovering power close to non-private benchmarks. |
| title | Gaussian Differentially Private $e$-values: Construction, Threshold Calibration, and Multiple Testing |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.29388 |