A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation, and Blackwell's Theorem

Differential privacy is widely considered the formal privacy for privacypreserving data analysis due to its robust and rigorous guarantees, with increasingly broad adoption in public services, academia, and industry. Although differential privacy originated in the cryptographic context, in this review we argue that, fundamentally, it can be considered a pure statistical concept. We leverage Blackwell's informativeness theorem and focus on demonstrating based on prior work that all definitions of differential privacy can be formally motivated from a hypothesis testing perspective, thereby showing that hypothesis testing is not merely convenient but also the right language for reasoning about differential privacy. This insight leads to the definition off-differential privacy, which extends other differential privacy definitions through a representation theorem. We review techniques that render f-differential privacy a unified framework for analyzing privacy bounds in data analysis and machine learning. Applications of this differential privacy definition to private deep learning, private convex optimization, shuffled mechanisms, and US Census data are discussed to highlight the benefits of analyzing privacy bounds under this framework compared with existing alternatives.