2021
DOI: 10.48550/arxiv.2111.12981
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Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

Samuel B. Hopkins,
Gautam Kamath,
Mahbod Majid

Abstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution with bounded covariance from Õ(d) independent samples subject to pure differential privacy. Prior algorithms for this problem either incur exponential running time, require Ω(d 1.5 ) samples, or satisfy only the weaker concentrated or approximate differential privacy conditions. In particular, all prior polynomial-time algorithms require d 1+Ω(1) samples to guarantee small privacy loss with "cryptographical… Show more

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