International Association
for Cryptologic Research

We introduce a generalization of differential privacy called \\emph{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 \\emph{outlier privacy}: an individual\'s privacy parameter is determined by how much of an ``\\emph{outlier}\'\' the individual is. We provide a new definition of an outlier and use it to introduce our notion of outlier privacy. Roughly speaking, \\emph{$\\eps(\\cdot)$-outlier privacy} requires that each individual in the data set is guaranteed ``$\\eps(k)$-differential privacy protection\'\', where $k$ is a number quantifying the ``outlierness\'\' of the individual. We demonstrate how to release accurate histograms that satisfy $\\eps(\\cdot)$-outlier privacy for various natural choices of $\\eps(\\cdot)$. Additionally, we show that $\\eps(\\cdot)$-outlier privacy with our weakest choice of $\\eps(\\cdot)$---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.