# Auditing Differential Privacy in High Dimensions with the Kernel Quantum R'enyi Divergence

arXiv: https://arxiv.org/abs/2205.13941 · HTML: https://mlsanity.com/paper/2205.13941/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [White-box vs Black-box: Bayes Optimal Strategies for Membership Inference](https://mlsanity.com/paper/1908.11229/) (2019)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Auditing Differentially Private Machine Learning: How Private is Private SGD?](https://mlsanity.com/paper/2006.07709/) (2020)
- [Detecting Violations of Differential Privacy](https://mlsanity.com/paper/1805.10277/) (2018)
- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [Minimax Optimal Estimation of KL Divergence for Continuous Distributions](https://mlsanity.com/paper/2002.11599/) (2020)
- [Nonparametric Estimation of Renyi Divergence and Friends](https://mlsanity.com/paper/1402.2966/) (2014)
- [Capacity Bounded Differential Privacy](https://mlsanity.com/paper/1907.02159/) (2019)

## Built on by (most cited first, 3 of 3)

- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [Sequentially Auditing Differential Privacy](https://mlsanity.com/paper/2509.07055/) (2025)
- [Picture the Epsilon: Pursuing Identity-Level Privacy Guarantees for Images](https://mlsanity.com/paper/2608.17147/) (2026)

## Abstract (arXiv)

Differential privacy (DP) is the de facto standard for private data release and private machine learning. Auditing black-box DP algorithms and mechanisms to certify whether they satisfy a certain DP guarantee is challenging, especially in high dimension. We propose relaxations of differential privacy based on new divergences on probability distributions: the kernel R'enyi divergence and its regularized version. We show that the regularized kernel R'enyi divergence can be estimated from samples even in high dimensions, giving rise to auditing procedures for varepsilon-DP, (varepsilon,δ)-DP and (α,varepsilon)-R'enyi DP.