The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at expense accuracy. In this paper, we investigate tradeoff between accuracy and mean estimation linear regression, under both classical low-dimensional modern high-dimensional settings. A primary focus to establish minimax optimality for with (ε,δ)-differential constraint. By refining “tracing adversary” technique lower bounds theoretical computer science literature, improve existing bound new regression problems. We also design differentially private algorithms that attain up logarithmic factors. particular, novel iterative hard thresholding algorithm proposed. The numerical performance demonstrated by simulation studies applications real sets.