Robustness Implies Privacy in Statistical Estimation

• URL: http://arxiv.org/abs/2212.05015v3
• Date: Sat, 15 Jun 2024 05:37:41 GMT
• Title: Robustness Implies Privacy in Statistical Estimation
• Authors: Samuel B. Hopkins, Gautam Kamath, Mahbod Majid, Shyam Narayanan,
• Abstract summary: We study the relationship between adversarial and differential privacy in high-dimensional statistics. We give the first blackbox reduction from privacy to robustness which can produce private estimators with optimal tradeoffs. Our algorithms are also robust to a nearly optimal fraction of adversarially-corrupted samples.
• Score: 16.061651295129302
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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