Differential privacy is widely considered the formal privacy for privacy-preserving data analysis due to its robust and rigorous guarantees, with increasingly broad adoption in public services, academia, and industry. Despite originating in the cryptographic context, in this review paper we argue that, fundamentally, differential privacy can be considered a \textit{pure} statistical concept. By leveraging a theorem due to David Blackwell, our focus is to demonstrate that the definition 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 of $f$-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 U.S.~Census data are discussed to highlight the benefits of analyzing privacy bounds under this framework compared to existing alternatives.

本研究解决了差分隐私作为一种统计概念的理解和应用的不足，提出了通过假设检验的视角重新定义差分隐私的必要性。文章引入了$f$-差分隐私的概念，并通过表征定理扩展了现有的差分隐私定义，提供了一个统一的框架用于分析数据分析和机器学习中的隐私界限。研究发现，这种框架在私有深度学习和其他应用中显示出相较于现有方法的显著优势。

从统计学角度看差分隐私：假设检验、表征与布莱克韦尔定理