# Fiducial Matching: Differentially Private Inference for Categorical Data

arXiv: https://arxiv.org/abs/2507.11762 · HTML: https://mlsanity.com/paper/2507.11762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 18 of 18)

- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020)
- [Differentially Private Bayesian Inference for Exponential Families](https://mlsanity.com/paper/1809.02188/) (2018)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism](https://mlsanity.com/paper/2208.06803/) (2022)
- [Data Augmentation MCMC for Bayesian Inference from Privatized Data](https://mlsanity.com/paper/2206.00710/) (2022)
- [Hypothesis Testing for Differentially Private Linear Regression](https://mlsanity.com/paper/2206.14449/) (2022)
- [Simulation-based, Finite-sample Inference for Privatized Data](https://mlsanity.com/paper/2303.05328/) (2023)
- [Private Posterior distributions from Variational approximations](https://mlsanity.com/paper/1511.07896/) (2015)
- [Repro Samples Method for Finite- and Large-Sample Inferences](https://mlsanity.com/paper/2206.06421/) (2022)
- [A New Class of Private Chi-Square Tests](https://mlsanity.com/paper/1610.07662/) (2016)
- [An accurate percentile method for parametric inference based on asymptotically biased estimators](https://mlsanity.com/paper/2405.05403/) (2024)
- [A General Approach for Simulation-based Bias Correction in High Dimensional Settings](https://mlsanity.com/paper/2010.13687/) (2020)
- [Just Identified Indirect Inference Estimator: Accurate Inference through Bias Correction](https://mlsanity.com/paper/2204.07907/) (2022)

## Built on by (most cited first, 1 of 1)

- [Equivalence Testing Under Privacy Constraints](https://mlsanity.com/paper/2604.06499/) (2026)

## Abstract (arXiv)

The task of statistical inference, which includes the building of confidence intervals and tests for parameters and effects of interest to a researcher, is still an open area of investigation in a differentially private (DP) setting. Indeed, in addition to the randomness due to data sampling, DP delivers another source of randomness consisting of the noise added to protect an individual's data from being disclosed to a potential attacker. As a result of this convolution of noises, in many cases it is too complicated to determine the stochastic behavior of the statistics and parameters resulting from a DP procedure. In this work, we contribute to this line of investigation by employing a simulation-based matching approach, solved through tools from the fiducial framework, which aims to replicate the data generation pipeline (including the DP step) and retrieve an approximate distribution of the estimates resulting from this pipeline. For this purpose, we focus on the analysis of categorical (nominal) data that is common in national surveys, for which sensitivity is naturally defined, and on additive privacy mechanisms. We prove the validity of the proposed approach in terms of coverage and highlight its good computational and statistical performance for different inferential tasks in simulated and applied data settings.