Robust and Differentially Private Mean Estimation

• DOI: 10.48550/arxiv.2102.09159
• Publication Date: 2021-01-01
• Authors: Liu, Xiyang; Kong, Weihao; Kakade, Sham; Oh, Sewoong
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; Computer Science - Cryptography and Security; Statistics - Machine Learning; Computer Science - Information Theory; Information Theory (cs.IT); 0202 electrical engineering, electronic engineering, information engineering; Machine Learning (stat.ML); 02 engineering and technology; Cryptography and Security (cs.CR); Machine Learning (cs.LG)

58 pages, 2 figures, both exponential time and efficient algorithms no longer require a known bound on the true mean<br/>In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual should be able to contribute without the fear of leaking one's sensitive information. At the same time, the system should be robust in the presence of malicious participants inserting corrupted data. Recent algorithmic advances in learning from shared data focus on either one of these threats, leaving the system vulnerable to the other. We bridge this gap for the canonical problem of estimating the mean from i.i.d. samples. We introduce PRIME, which is the first efficient algorithm that achieves both privacy and robustness for a wide range of distributions. We further complement this result with a novel exponential time algorithm that improves the sample complexity of PRIME, achieving a near-optimal guarantee and matching a known lower bound for (non-robust) private mean estimation. This proves that there is no extra statistical cost to simultaneously guaranteeing privacy and robustness.<br/>