Designing Differentially Private Estimators in High Dimensions

TL;DR

This paper introduces a computationally efficient high-dimensional differentially private mean estimator with dimension-independent privacy guarantees, outperforming classic methods on synthetic data.

Contribution

It leverages robust statistics to bound sensitivity and develop a scalable, privacy-preserving mean estimation algorithm for high-dimensional data.

Findings

Outperforms classic differential privacy methods on synthetic data

Achieves dimension-independent privacy loss

Provides a tractable algorithm for high-dimensional mean estimation

Abstract

We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss. Recent work in high-dimensional robust statistics has identified computationally tractable mean estimation algorithms with asymptotic dimension-independent error guarantees. We incorporate these results to develop a strict bound on the global sensitivity of the robust mean estimator. This yields a computationally tractable algorithm for differentially private mean estimation in high dimensions with dimension-independent privacy loss. Finally, we show on synthetic data that our algorithm significantly outperforms classic differential privacy methods, overcoming barriers to high-dimensional differential privacy.