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

arXiv: https://arxiv.org/abs/2409.09558 · HTML: https://mlsanity.com/paper/2409.09558/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 61 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 30 of 35)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Privacy Amplification by Iteration](https://mlsanity.com/paper/1808.06651/) (2018)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Federated Learning of Gboard Language Models with Differential Privacy](https://mlsanity.com/paper/2305.18465/) (2023)
- [Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Loss](https://mlsanity.com/paper/2205.13710/) (2022)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [SoK: Differential Privacies](https://mlsanity.com/paper/1906.01337/) (2019)
- [Federated f-Differential Privacy](https://mlsanity.com/paper/2102.11158/) (2021)
- [Stronger Privacy Amplification by Shuffling for R'enyi and Approximate Differential Privacy](https://mlsanity.com/paper/2208.04591/) (2022)
- [Advancing Differential Privacy: Where We Are Now and Future Directions for Real-World Deployment](https://mlsanity.com/paper/2304.06929/) (2023)
- [LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale](https://mlsanity.com/paper/2002.05839/) (2020)
- [Edgeworth Accountant: An Analytical Approach to Differential Privacy Composition](https://mlsanity.com/paper/2206.04236/) (2022)
- [Unified Enhancement of Privacy Bounds for Mixture Mechanisms via f-Differential Privacy](https://mlsanity.com/paper/2310.19973/) (2023)
- [Shifted Interpolation for Differential Privacy](https://mlsanity.com/paper/2403.00278/) (2024)
- [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021)
- [A Central Limit Theorem for Differentially Private Query Answering](https://mlsanity.com/paper/2103.08721/) (2021)

## Built on by (most cited first, 8 of 8)

- [Unifying Re-Identification, Attribute Inference, and Data Reconstruction Risks in Differential Privacy](https://mlsanity.com/paper/2507.06969/) (2025)
- [The 2020 US Decennial Census is more private than you (might) think](https://mlsanity.com/paper/2410.09296/) (2024)
- [Setting varepsilon is not the Issue in Differential Privacy](https://mlsanity.com/paper/2511.06305/) (2025)
- [Robust and Differentially Private Principal Component Analysis](https://mlsanity.com/paper/2507.15232/) (2025)
- [Differential privacy from axioms](https://mlsanity.com/paper/2511.21876/) (2025)
- [A Sieve-Accelerated Quadrature Method for Exact Privacy Accounting in the 2020 U.S. Decennial Census](https://mlsanity.com/paper/2606.29835/) (2026)
- [Deciding When to Switch: E-Processes for Adaptive Minimax Training for Generative Adversarial Nets](https://mlsanity.com/paper/2608.10096/) (2026)
- [Algorithmic stability via ensembling](https://mlsanity.com/paper/2609.10428/) (2026)

## Abstract (arXiv)

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 textitpure statistical concept. By leveraging David Blackwell's informativeness theorem, our focus is to demonstrate 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 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.