Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908521053814784 |
|---|---|
| author | Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi |
| author_facet | Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi |
| contents | In this paper, we study the problem of estimating the variance and covariance of datasets under differential privacy in the add-remove model. While estimation in the swap model has been extensively studied in the literature, the add-remove model remains less explored and more challenging, as the dataset size must also be kept private. To address this issue, we develop efficient mechanisms for variance and covariance estimation based on the \emph{Bézier mechanism}, a novel moment-release framework that leverages Bernstein bases. We prove that our proposed mechanisms are minimax optimal in the high-privacy regime by establishing new minimax lower bounds. Moreover, beyond worst-case scenarios, we analyze instance-wise utility and show that the Bézier-based estimator consistently achieves better utility compared to alternative mechanisms. Finally, we demonstrate the effectiveness of the Bézier mechanism beyond variance and covariance estimation, showcasing its applicability to other statistical tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond Takakura, Shokichi Liew, Seng Pei Hasegawa, Satoshi Machine Learning Data Structures and Algorithms In this paper, we study the problem of estimating the variance and covariance of datasets under differential privacy in the add-remove model. While estimation in the swap model has been extensively studied in the literature, the add-remove model remains less explored and more challenging, as the dataset size must also be kept private. To address this issue, we develop efficient mechanisms for variance and covariance estimation based on the \emph{Bézier mechanism}, a novel moment-release framework that leverages Bernstein bases. We prove that our proposed mechanisms are minimax optimal in the high-privacy regime by establishing new minimax lower bounds. Moreover, beyond worst-case scenarios, we analyze instance-wise utility and show that the Bézier-based estimator consistently achieves better utility compared to alternative mechanisms. Finally, we demonstrate the effectiveness of the Bézier mechanism beyond variance and covariance estimation, showcasing its applicability to other statistical tasks. |
| title | Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2509.04919 |