Privacy-Preserving Bayesian Inference: Foundations and Extensions

This project provides a theoretical foundation and computational methodologies to conduct Bayesian statistical inference using differentially private data. Differential privacy is a mathematical framework that allows the release of potentially sensitive data in such a way that protects the confidentiality of individual records without unduly sacrificing its overall usefulness for statistical analysis. As our society today grapples with the privacy implications that accompany the exploding growth of large-scale datasets, the invention of differential privacy provides a solution to protect personal demographic and biological information without deterring the accumulation of public knowledge. The U.S. Census Bureau has officially adopted differential privacy as the disclosure avoidance method for the 2020 Census. Other data collectors and curators are expected to follow suit in the near future. This project answers the pressing need for new statistical theory and methods to appropriately understand and efficiently analyze differentially private data. The project will expand the repertoire of tools available to researchers, and contribute to the cause of creating a better informed and more transparent society while respecting individual privacy.

The PI will work on a theoretical formulation of the definitions of differential privacy using imprecise probability constructions, including interval of measures and coherent upper-lower probability measures. In the Bayesian context, such a formulation delivers a robust-likelihood conception of the model and allows for the computation of bounds on posterior quantities based on differentially private data for arbitrary prior specifications. The PI also proposes the differentially private approximate Bayesian computation (ABC) algorithm, a noisy ABC algorithm that delivers exact posterior inference given differentially private observations subject to arbitrary additive noise. The algorithm permits differentially private inference from large-scale Bayesian models with intractable likelihoods. The project bridges the classic theories of robust Bayes and generalized Bayes, with the novel literature on statistical privacy, and derives practical implementations based on privacy-preserving data releases. The project will supply analysts and researchers in a timely fashion with inferential methodologies tailored for differentially private input that are both theoretically sound and computationally efficient.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.