# Unified Mechanism-Specific Amplification by Subsampling and Group Privacy Amplification

arXiv: https://arxiv.org/abs/2403.04867 · HTML: https://mlsanity.com/paper/2403.04867/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2024.

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

- [Differentially Private Relational Learning with Entity-level Privacy Guarantees](https://mlsanity.com/paper/2506.08347/) (2025)
- [Provable Robustness against Backdoor Attacks via the Primal-Dual Perspective on Differential Privacy](https://mlsanity.com/paper/2605.21780/) (2026)
- [Dithered Gaussian Mechanism for Randomness-Efficient Differential Privacy](https://mlsanity.com/paper/2607.06320/) (2026)

## Abstract (arXiv)

Amplification by subsampling is one of the main primitives in machine learning with differential privacy (DP): Training a model on random batches instead of complete datasets results in stronger privacy. This is traditionally formalized via mechanism-agnostic subsampling guarantees that express the privacy parameters of a subsampled mechanism as a function of the original mechanism's privacy parameters. We propose the first general framework for deriving mechanism-specific guarantees, which leverage additional information beyond these parameters to more tightly characterize the subsampled mechanism's privacy. Such guarantees are of particular importance for privacy accounting, i.e., tracking privacy over multiple iterations. Overall, our framework based on conditional optimal transport lets us derive existing and novel guarantees for approximate DP, accounting with R'enyi DP, and accounting with dominating pairs in a unified, principled manner. As an application, we analyze how subsampling affects the privacy of groups of multiple users. Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.