Outlier privacy

We introduce a generalization of differential privacy called tailored differential privacy, where an individual’s privacy parameter is “tailored” for the individual based on the individual’s data and the data set. In this paper, we focus on a natural instance of tailored differential privacy, which we call outlier privacy: an individual’s privacy parameter is determined by how much of an “outlier” the individual is. We provide a new definition of an outlier and use it to introduce our notion of outlier privacy. Roughly speaking, Є(·)-outlier privacy requires that each individual in the data set is guaranteed “Є(k)-differential privacy protection”, where k is a number quantifying the “outlierness” of the individual. We demonstrate how to release accurate histograms that satisfy Є(·)-outlier privacy for various natural choices of Є(·). Additionally, we show that Є(·)-outlier privacy with our weakest choice of Є(·)—which offers no explicit privacy protection for “non-outliers”—already implies a “distributional” notion of differential privacy w.r.t. a large and natural class of distributions.