High-Probability Bounds For Heterogeneous Local Differential Privacy
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915552936591360 |
|---|---|
| author | Aliakbarpour, Maryam Fallah, Alireza Roy, Swaha Stevens, Ria |
| author_facet | Aliakbarpour, Maryam Fallah, Alireza Roy, Swaha Stevens, Ria |
| contents | We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-β$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Probability Bounds For Heterogeneous Local Differential Privacy Aliakbarpour, Maryam Fallah, Alireza Roy, Swaha Stevens, Ria Machine Learning Cryptography and Security Data Structures and Algorithms We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-β$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels. |
| title | High-Probability Bounds For Heterogeneous Local Differential Privacy |
| topic | Machine Learning Cryptography and Security Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.11895 |