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Activity Number: 174 - Statistical Optimality in High-Dimensional Models and Tradeoffs with Computational Complexity, Privacy and Communication Constraints
Type: Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
Sponsor: IMS
Abstract #309742
Title: The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacy
Author(s): Yichen Wang* and Tony Cai and Linjun Zhang
Companies: The Wharton School, University of Pennsylvania and University of Pennsylvania and Rutgers University
Keywords: Differential privacy; High-dimensional data; Minimax optimality
Abstract:

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this talk, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low- dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the differential privacy constraint. To this end, we find that classical lower bound arguments fail to yield sharp results, and new technical tools are called for. By refining the ``tracing adversary" technique for lower bounds in the theoretical computer science literature, we formulate a general lower bound argument for minimax risks with differential privacy constraints, and apply this argument to high-dimensional mean estimation and linear regression problems. We also design computationally efficient algorithms that attain the minimax lower bounds up to a logarithmic factor.


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