New Statistical Applications for Differential Privacy
Rob Hall · 2013
Differential privacy is a relatively recent development in the field of privacy-preserving data mining, which was formulated to give a mathematically rigorous definition of privacy. The concept has spawned a great deal of work regarding the development of algorithms which are privacy-preserving under this definition, and also work which seeks to understand the fundamental limitations of such algorithms. When the goal is statistical inference it is important to understand what set of analyses may be carried out in the privacy-preserving framework with reasonable accuracy, and which data summaries and results may be reported. In this work we begin by examining fundamental limitations of differentially private procedures when the goal is to release a sparse histogram, or a contingency table. We also describe error bounds when the goal is model selection for a private contingency table. Through examples we will demonstrate the implications of these lower error bounds for statistical analysis with datasets of different sizes and dimensions. Thus far, differentially private algorithms appear to be restricted to the release of finite dimensional vectors (e.g., regression coefficients, point estimates, SVM parameters). We next develop methods for releasing functional data while preserving differential privacy. Specifically, we show