Efficient Bayesian Computations for Inference from Privatized Data

Privacy-preserving data analysis is essential for modern data science. While governments, businesses, and researchers frequently collect data to advance science and inform decisions that affect our health and daily lives, people increasingly demand the protection of their sensitive information during data collection and analysis. Local differential privacy ensures this by allowing each person to add random noise to their response before sharing it, so the original sensitive data never needs to be stored. However, due to local perturbations, it is now harder for data analysts to extract accurate insights from the privatized data, necessitating new statistical methods for their analysis. This project aims to develop Bayesian inference and computational tools to analyze locally privatized data, and the proposed research advances the frontiers of responsible data science, differential privacy, and Bayesian statistics. The project also provides research opportunities for graduate students. This project develops Bayesian statistical methods and algorithms that can reliably analyze data protected by local privacy, with a focus on computational efficiency and scalability. The research proposes a novel framework that incorporates the privatization process into Bayesian modeling and thus properly accounts for privacy noise in uncertainty quantification. The project will develop both new sampling and variational inference methods, and theoretically and empirically investigate their convergence and concentration properties. By enabling Bayesian inference from privatized data, the developed methods can unleash the potential of many existing privatized datasets. The theory, methods, and software from this project will advance privacy-preserving algorithm design and clarify their limits. This foundational work will pave the way for practical tools that enable governments, businesses, and researchers to answer critical questions without compromising individual privacy. 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.