Local Privacy and Statistical Minimax Rates

Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. When combined with minimax techniques such as Le Cam's and Fano's methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints. In this paper, we provide a treatment of two canonical problem families: mean estimation in location…

• ND
  National Defense Science and Engineering Graduate
• MU
  Multidisciplinary University Research Initiative
• OO
  Office of Naval Research
• AR
  Army Research Office
• AR
  Army Research Laboratory