Journal Article

A Statistical Framework for Differential Privacy

Wasserman, Larry, Zhou, Shuheng

2010

Overview

One goal of statistical privacy research is to construct a data release mechanism that protects individual privacy while preserving information content. An example is a random mechanism that takes an input database X and outputs a random database Z according to a distribution Q n (⋅|X). Differential privacy is a particular privacy requirement developed by computer scientists in which Q n (⋅|X) is required to be insensitive to changes in one data point in X. This makes it difficult to infer from Z whether a given individual is in the original database X. We consider differential privacy from a statistical perspective. We consider several data-release mechanisms that satisfy the differential privacy requirement. We show that it is useful to compare these schemes by computing the rate of convergence of distributions and densities constructed from the released data. We study a general privacy method, called the exponential mechanism, introduced by McSherry and Talwar (2007). We show that the accuracy of this method is intimately linked to the rate at which the probability that the empirical distribution concentrates in a small ball around the true distribution.

• Publisher: Taylor & Francis,American Statistical Association,Assoc,Taylor & Francis Ltd
• Subject: Convergence / Cubes / Data analysis / Density estimation / Differential analysis / Disclosure limitation / Distribution / Distribution functions / Estimating techniques / Estimators / Histograms / Information content / Legal proceedings / Minimax / Minimax estimation / Privacy / Privacy protection / Statistical analysis / Statistical data / Statistical decision / Statistical methods / Statistical theories / Statistics / Theory and Methods / Triangle inequalities