A Bias-Accuracy-Privacy Trilemma for Statistical Estimation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929530642366464 |
|---|---|
| author | Kamath, Gautam Mouzakis, Argyris Regehr, Matthew Singhal, Vikrant Steinke, Thomas Ullman, Jonathan |
| author_facet | Kamath, Gautam Mouzakis, Argyris Regehr, Matthew Singhal, Vikrant Steinke, Thomas Ullman, Jonathan |
| contents | Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their empirical mean. Clipping controls the sensitivity and, hence, the variance of the noise that we add for privacy. But clipping also introduces statistical bias. This tradeoff is inherent: we prove that no algorithm can simultaneously have low bias, low error, and low privacy loss for arbitrary distributions.
Additionally, we show that under strong notions of DP (i.e., pure or concentrated DP), unbiased mean estimation is impossible, even if we assume that the data is sampled from a Gaussian. On the positive side, we show that unbiased mean estimation is possible under a more permissive notion of differential privacy (approximate DP) if we assume that the distribution is symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Bias-Accuracy-Privacy Trilemma for Statistical Estimation Kamath, Gautam Mouzakis, Argyris Regehr, Matthew Singhal, Vikrant Steinke, Thomas Ullman, Jonathan Statistics Theory Cryptography and Security Data Structures and Algorithms Machine Learning Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their empirical mean. Clipping controls the sensitivity and, hence, the variance of the noise that we add for privacy. But clipping also introduces statistical bias. This tradeoff is inherent: we prove that no algorithm can simultaneously have low bias, low error, and low privacy loss for arbitrary distributions. Additionally, we show that under strong notions of DP (i.e., pure or concentrated DP), unbiased mean estimation is impossible, even if we assume that the data is sampled from a Gaussian. On the positive side, we show that unbiased mean estimation is possible under a more permissive notion of differential privacy (approximate DP) if we assume that the distribution is symmetric. |
| title | A Bias-Accuracy-Privacy Trilemma for Statistical Estimation |
| topic | Statistics Theory Cryptography and Security Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2301.13334 |