Advancements in Gaussian and Local Differential Privacy

Abstract

This thesis presents a comprehensive study of Gaussian Differential Privacy (GDP) and Local Differential Privacy (LDP), exploring their properties, relationships, and applications in developing novel algorithms and optimization methods for efficient and accurate privacy-preserving data analysis. In the first paper, we examine asymptotic properties of privacy profiles, develop a criterion for identifying GDP algorithms, propose an efficient method for narrowing down optimal privacy measurement values, and introduce a post-processing procedure for non-GDP algorithms. We also compare single-parameter privacy notions and demonstrate the advantages of our measurement process and the composition theorem of GDP. The second paper focuses on estimating population quantiles under LDP using binary inquiries, developing a self-normalizing, online algorithm with valid inference and optimality results for median estimation. The third paper introduces a novel algorithm for estimating Cumulative Distribution Function (CDF) curves under LDP by combining constrained isotonic estimation and binary inquiries, uncovering an unexpected connection to the current status problem in survival data analysis. We establish error bounds and computational efficiency for our estimator. Collectively, these papers contribute to the understanding and development of efficient, privacy-preserving mechanisms in GDP and LDP, providing valuable insights and practical tools for data analysts and privacy researchers, and advancing the state of the art in differential privacy research.