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Local Privacy and Statistical Minimax Rates
Abstract
Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. When combined with minimax techniques such as Le Cam's and Fano's methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints. In this paper, we provide a treatment of two canonical problem families: mean estimation in location family models and convex risk minimization. For these families, we provide lower and upper bounds for estimation of population quantities that match up to constant factors, giving privacy-preserving mechanisms and computationally efficient estimators that achieve the bounds.
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Cited by
Advances and Open Problems in Federated Learning
Kairouz, P., & McMahan, H. B. (2021) · Foundations and Trends in Machine Learning · doi:10.1561/2200000083 · Cited by 7,772
“While LDP protocols are effective at enforcing privacy and have theoretical justifications [156, 135, 136], a number of results have shown that achieving local differential privacy while preserving utility is challenging particularly, especially in high-dimensional data settings [229, 388, 219, 51, 220, 424, 142, 111].”
BackgroundPractical Secure Aggregation for Privacy-Preserving Machine Learning
Bonawitz, K., Ivanov, V., Kreuter, B., Marcedone, A., McMahan, H. B., Patel, S., Ramage, D., Segal, A., & Seth, K. (2017) · Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security · doi:10.1145/3133956.3133982 · Cited by 3,956
Mironov, I. (2017) · 2017 IEEE 30th Computer Security Foundations Symposium (CSF) · doi:10.1109/csf.2017.11 · Cited by 1,255
Privacy and Robustness in Federated Learning: Attacks and Defenses
Lyu, L., Yu, H., Ma, X., Chen, C., Sun, L., Zhao, J., Yang, Q., & Yu, P. S. (2024) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2022.3216981 · Cited by 548
Differential Privacy for Deep and Federated Learning: A Survey
Ouadrhiri, A. E., & Abdelhadi, A. (2022) · IEEE Access · doi:10.1109/access.2022.3151670 · Cited by 445
Metadata
- Authors
- Duchi, J. C., Jordan, M. I., & Wainwright, M. J.
- Venue
- 2013 IEEE 54th Annual Symposium on Foundations of Computer Science
- Publisher
- IEEE
- Published
- 2013-10
- Pages
- 429-438
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2053801139
- Cited by
- 954
- References
- 2
- FWCI
- 17.35
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Duchi, J. C., Jordan, M. I., & Wainwright, M. J. (2013). Local Privacy and Statistical Minimax Rates. 2013 IEEE 54th Annual Symposium on Foundations of Computer Science. https://doi.org/10.1109/focs.2013.53
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