Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
نویسندگان
چکیده
We provide a detailed study of the estimation of probability distributions— discrete and continuous—in a stringent setting in which data is kept private even from the statistician. We give sharp minimax rates of convergence for estimation in these locally private settings, exhibiting fundamental trade-offs between privacy and convergence rate, as well as providing tools to allow movement along the privacy-statistical efficiency continuum. One of the consequences of our results is that Warner’s classical work on randomized response is an optimal way to perform survey sampling while maintaining privacy of the respondents.
منابع مشابه
Local Privacy, Data Processing Inequalities, and Statistical Minimax Rates
Working under a model of privacy in which data remains private even from the statistician, 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 depend on the privacy guarantees. When combined with standard minimax techniques...
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