Weijie Su, University of Pennsylvania
Title: A Statistical Viewpoint on Privacy: From Hypothesis Testing to Blackwell鈥檚 Theorem
Date: Friday, September 20th, 2024
Time: 1:15PM (PDT)
Location: ASB 10900
Abstract:
Privacy-preserving data analysis has been put on a firm mathematical foundation since the introduction of differential privacy (DP) in 2006. This privacy definition, however, has some well-known weaknesses: notably, it does not tightly handle composition. In this talk, we propose a relaxation of DP termed "f-DP", which offers several appealing properties and avoids some difficulties associated with prior relaxations. This approach allows for lossless reasoning about composition and post-processing, and notably, provides a direct way to analyze privacy amplification by subsampling. These desiderata of f-DP are enabled by applying a theorem of David Blackwell to the hypothesis testing formulation of DP. We define a canonical single-parameter family of definitions within our class called "Gaussian Differential Privacy", based on hypothesis testing of two shifted normal distributions. We prove that this family is focal to f-DP by introducing a central limit theorem, which shows that the privacy guarantees of any hypothesis-testing based definition of privacy converge to Gaussian DP in the limit under composition. Finally, we demonstrate the practical applications of these tools by presenting an improved analysis of privacy guarantees in private deep learning and the US 2020 decennial census.