# Hypothesis Testing Interpretations and Renyi Differential Privacy

arXiv: https://arxiv.org/abs/1905.09982 · HTML: https://mlsanity.com/paper/1905.09982/

## Key facts

- Cited by 85 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 30 of 85)

- [Reconstructing Training Data with Informed Adversaries](https://mlsanity.com/paper/2201.04845/) (2022)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Decentralized Federated Learning through Proxy Model Sharing](https://mlsanity.com/paper/2111.11343/) (2021)
- [TAN Without a Burn: Scaling Laws of DP-SGD](https://mlsanity.com/paper/2210.03403/) (2022)
- [Defending against Reconstruction Attacks with R'enyi Differential Privacy](https://mlsanity.com/paper/2202.07623/) (2022)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Federated f-Differential Privacy](https://mlsanity.com/paper/2102.11158/) (2021)
- [Certified Unlearning for Neural Networks](https://mlsanity.com/paper/2506.06985/) (2025)
- [CANIFE: Crafting Canaries for Empirical Privacy Measurement in Federated Learning](https://mlsanity.com/paper/2210.02912/) (2022)
- [Correlated Noise Provably Beats Independent Noise for Differentially Private Learning](https://mlsanity.com/paper/2310.06771/) (2023)
- [Differentially Private Next-Token Prediction of Large Language Models](https://mlsanity.com/paper/2403.15638/) (2024)
- [Have it your way: Individualized Privacy Assignment for DP-SGD](https://mlsanity.com/paper/2303.17046/) (2023)
- [Gaussian Membership Inference Privacy](https://mlsanity.com/paper/2306.07273/) (2023)
- [Unleashing the Power of Randomization in Auditing Differentially Private ML](https://mlsanity.com/paper/2305.18447/) (2023)
- [ViP: A Differentially Private Foundation Model for Computer Vision](https://mlsanity.com/paper/2306.08842/) (2023)
- [On the Renyi Differential Privacy of the Shuffle Model](https://mlsanity.com/paper/2105.05180/) (2021)
- [Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacy](https://mlsanity.com/paper/2307.03928/) (2023)
- [Federated Deep Learning with Bayesian Privacy](https://mlsanity.com/paper/2109.13012/) (2021)
- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [Shifted Interpolation for Differential Privacy](https://mlsanity.com/paper/2403.00278/) (2024)
- [Unraveling the Connections between Privacy and Certified Robustness in Federated Learning Against Poisoning Attacks](https://mlsanity.com/paper/2209.04030/) (2022)
- [Improving the Privacy and Practicality of Objective Perturbation for Differentially Private Linear Learners](https://mlsanity.com/paper/2401.00583/) (2023)
- [Preserving Node-level Privacy in Graph Neural Networks](https://mlsanity.com/paper/2311.06888/) (2023)
- [Improving Privacy-Preserving Vertical Federated Learning by Efficient Communication with ADMM](https://mlsanity.com/paper/2207.10226/) (2022)
- [DPSUR: Accelerating Differentially Private Stochastic Gradient Descent Using Selective Update and Release](https://mlsanity.com/paper/2311.14056/) (2023)
- [Data-adaptive Differentially Private Prompt Synthesis for In-Context Learning](https://mlsanity.com/paper/2410.12085/) (2024)
- [InvisibleInk: High-Utility and Low-Cost Text Generation with Differential Privacy](https://mlsanity.com/paper/2507.02974/) (2025)
- [ULDP-FL: Federated Learning with Across Silo User-Level Differential Privacy](https://mlsanity.com/paper/2308.12210/) (2023)
- [DP-DyLoRA: Fine-Tuning Transformer-Based Models On-Device under Differentially Private Federated Learning using Dynamic Low-Rank Adaptation](https://mlsanity.com/paper/2405.06368/) (2024)

## Abstract (arXiv)

Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectively test whether a specific individual has contributed her data by observing the output of a private mechanism---any test cannot have both high significance and high power. In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation. These conditions are useful to analyze the distinguishability power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Renyi divergence. This analysis also results in an improved conversion rule between these definitions and differential privacy.