Year: 2021
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: University of Washington
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: AF: Medium: Collaborative Research: Estimation, Learning, and Memory: The Quest for Statistically Optimal Algorithms, AI Institute for Future Edge Networks and Distributed Intelligence (AI-EDGE), Collaborative Research: MLWiNS: Physical Layer Communication revisited via Deep Learning, CIF: RI: Small: Information-theoretic measures of dependencies and novel sample-based estimators, CIF: Medium: Anonymous Broadcasting over Networks: Fundamental Limits and Algorithms, AI Institute: Institute for Foundations of Machine Learning
OpenAlex ID: W3130328209