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

• URL: http://arxiv.org/abs/2603.02010v1
• Date: Mon, 02 Mar 2026 15:55:54 GMT
• Title: Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families
• Authors: Amir Asiaee, Samhita Pal,
• Abstract summary: Many differentially private (DP) data release systems either output DP synthetic data or leave analysts to perform inference as usual.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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