A Statistical Framework for Differential Privacy

Abstract

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.

Differential Privacy for Statistics: What we Know and What we Want to Learn

“…The argument we have just given can be interpreted in terms hypothesis testing; see, for example, Wasserman and Zhou [62] for more discussion.…”

“…Even more recently, Wasserman and Zhou [62] considered differentially-private nonparametric techniques. That work came to our attention after the initial version of this survey was written; we do not discuss it in detail here, except to note that certain nonparametric techniques, such as historgram-based estimation, are directly amenable to the sensitivity-based noise addition discussed above.…”

“…More generally, one can sample from an appropriately constructed distribution on objects of interest [44], such as synthetic data sets [5,62]. These approaches are discussed further below.…”

“…We have shown that several parametric statistical estimators can incorporate differential privacy with little loss of accuracy. Non-parametric methods were addressed subsequently by Wasserman and Zhou [62]. We would like to see a library of differentially private versions of the algorithms in R and SAS.…”

Data Smearing: An Approach to Disclosure Limitation for Tabular Data

“…Because quantifying the level of protection and the utility a given DLM provides is difficult (Lambert 1993), comparing DLMs (and thus choosing a method) is not straightforward. Indeed, the level of protection offered by a DLM usually depends on characteristics of the data being published and is usually only quantified with certain restrictions on how the data can be accessed (see, for example Wasserman and Zhou 2010). Measures of the utility, on the other hand, often depend on the intended purpose of the data.…”