# Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families

arXiv: https://arxiv.org/abs/2603.02010 · HTML: https://mlsanity.com/paper/2603.02010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 2 Mar 2026.

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

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021)
- [AIM: An Adaptive and Iterative Mechanism for Differentially Private Synthetic Data](https://mlsanity.com/paper/2201.12677/) (2022)
- [Benchmarking Differentially Private Synthetic Data Generation Algorithms](https://mlsanity.com/paper/2112.09238/) (2021)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [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)
- [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Privacy-preserving data release leveraging optimal transport and particle gradient descent](https://mlsanity.com/paper/2401.17823/) (2024)
- [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)
- [Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?](https://mlsanity.com/paper/2403.13612/) (2024)

## Abstract (arXiv)

Many differentially private (DP) data release systems either output DP synthetic data and leave analysts to perform inference as usual, which can lead to severe miscalibration, or output a DP point estimate without a principled way to do uncertainty quantification. This paper develops a clean and tractable middle ground for exponential families: release only DP sufficient statistics, then perform noise-calibrated likelihood-based inference and optional parametric synthetic data generation as post-processing. Our contributions are: (1) a general recipe for approximate-DP release of clipped sufficient statistics under the Gaussian mechanism; (2) asymptotic normality, explicit variance inflation, and valid Wald-style confidence intervals for the plug-in DP MLE; (3) a noise-aware likelihood correction that is first-order equivalent to the plug-in but supports bootstrap-based intervals; and (4) a matching minimax lower bound showing the privacy distortion rate is unavoidable. The resulting theory yields concrete design rules and a practical pipeline for releasing DP synthetic data with principled uncertainty quantification, validated on three exponential families and real census data.