mlsanityData to 14 Oct 2026

Fiducial Matching: Differentially Private Inference for Categorical Data

arXiv 2507.11762 ↗First posted 15 Jul 2025stat.ME stat.CO stat.MLcited by 1

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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.

Key facts. Cited by 1 paper 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

18 of 42 references.

References · 18

  1. 2018Subsampled R'enyi Differential Privacy and Analytical Moments Accountantcited by 236
  2. 2018Protection Against Reconstruction and Its Applications in Private Federated Learningcited by 130
  3. 2018The Structure of Optimal Private Tests for Simple Hypothesescited by 26
  4. 2016Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testingcited by 24
  5. 2019Differentially Private Bayesian Linear Regressioncited by 24
  6. 2020Parametric Bootstrap for Differentially Private Confidence Intervalscited by 19
  7. 2018Differentially Private Bayesian Inference for Exponential Familiescited by 18
  8. 2023The Test of Tests: A Framework For Differentially Private Hypothesis Testingcited by 9
  9. 2022Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanismcited by 8
  10. 2022Data Augmentation MCMC for Bayesian Inference from Privatized Datacited by 7
  11. 2022Hypothesis Testing for Differentially Private Linear Regressioncited by 7
  12. 2023Simulation-based, Finite-sample Inference for Privatized Datacited by 7
6 more
  1. 2015Private Posterior distributions from Variational approximationscited by 4
  2. 2022Repro Samples Method for Finite- and Large-Sample Inferencescited by 4
  3. 2016A New Class of Private Chi-Square Testscited by 3
  4. 2024An accurate percentile method for parametric inference based on asymptotically biased estimatorscited by 2
  5. 2020A General Approach for Simulation-based Bias Correction in High Dimensional Settingscited by 1
  6. 2022Just Identified Indirect Inference Estimator: Accurate Inference through Bias Correctioncited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Equivalence Testing Under Privacy Constraintscited by 0