We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics. We give the first black-box reduction from privacy to robustness which can produce private estimators with optimal tradeoffs among sample complexity, accuracy, and privacy for a wide range of fundamental high-dimensional parameter estimation problems, including mean and covariance estimation. We show that this reduction can be implemented in polynomial time in some important special cases. In particular, using nearly-optimal polynomial-time robust estimators for the mean and covariance of high-dimensional Gaussians which are based on the Sum-of-Squares method, we design the first polynomial-time private estimators for these problems with nearly-optimal samples-accuracy-privacy tradeoffs. Our algorithms are also robust to a nearly optimal fraction of adversarially-corrupted samples.
CITATION STYLE
Hopkins, S. B., Kamath, G., Majid, M., & Narayanan, S. (2023). Robustness Implies Privacy in Statistical Estimation. In Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 497–506). Association for Computing Machinery. https://doi.org/10.1145/3564246.3585115
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