Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning

Abstract:Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and nonparametric regression over the Sobolev class.

Statistics Theory (math.ST); Cryptography and Security (cs.CR); Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)

arXiv:2303.07152 [math.ST]

(or arXiv:2303.07152v3 [math.ST] for this version)

https://doi.org/10.48550/arXiv.2303.07152 Focus to learn more arXiv-issued DOI via DataCite

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