# Simulation-based, Finite-sample Inference for Privatized Data

arXiv: https://arxiv.org/abs/2303.05328 · HTML: https://mlsanity.com/paper/2303.05328/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2023.

## Built on by (most cited first, 7 of 7)

- [Gaussian Differential Private Bootstrap by Subsampling](https://mlsanity.com/paper/2505.01197/) (2025)
- [Simulation-based Bayesian Inference from Privacy Protected Data](https://mlsanity.com/paper/2310.12781/) (2023)
- [Fiducial Matching: Differentially Private Inference for Categorical Data](https://mlsanity.com/paper/2507.11762/) (2025)
- [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025)
- [Flexible Selective Inference with Flow-based Transport Maps](https://mlsanity.com/paper/2506.01150/) (2025)
- [Near-Optimal Private Tests for Simple and MLR Hypotheses](https://mlsanity.com/paper/2601.21959/) (2026)
- [Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families](https://mlsanity.com/paper/2603.02010/) (2026)

## Abstract (arXiv)

Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests, which builds on the work of Xie and Wang (2022). We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and p-values.