Optimal Debiased Inference on Privatized Data via Indirect Estimation and Parametric Bootstrap

2025-07-14

AI Summary

Existing differentially private statistical inference methods often neglect the impact of data clamping on the sampling distribution of estimators, leading to undercoverage of confidence intervals and uncontrolled Type-I error rates in hypothesis testing. To address this, we propose a debiased parametric bootstrap framework that—novelty—integrates indirect estimation with adaptive simulation to invert the clamping mechanism, yielding consistent and asymptotically minimum-variance estimators of the original parameters. Our approach obviates explicit modeling of clamping thresholds and applies broadly to canonical settings including location-scale normal models, linear regression, and logistic regression. We establish theoretical guarantees that the method exactly calibrates confidence interval coverage probabilities and hypothesis test significance levels under differential privacy. Empirical evaluations demonstrate substantial finite-sample improvements over state-of-the-art baselines.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We design a debiased parametric bootstrap framework for statistical inference from differentially private data. Existing usage of the parametric bootstrap on privatized data ignored or avoided handling the effect of clamping, a technique employed by the majority of privacy mechanisms. Ignoring the impact of clamping often leads to under-coverage of confidence intervals and miscalibrated type I errors of hypothesis tests. The main reason for the failure of the existing methods is the inconsistency of the parameter estimate based on the privatized data. We propose using the indirect inference method to estimate the parameter values consistently, and we use the improved estimator in parametric bootstrap for inference. To implement the indirect estimator, we present a novel simulation-based, adaptive approach along with the theory that establishes the consistency of the corresponding parametric bootstrap estimates, confidence intervals, and hypothesis tests. In particular, we prove that our adaptive indirect estimator achieves the minimum asymptotic variance among all "well-behaved" consistent estimators based on the released summary statistic. Our simulation studies show that our framework produces confidence intervals with well-calibrated coverage and performs hypothesis testing with the correct type I error, giving state-of-the-art performance for inference on location-scale normals, simple linear regression, and logistic regression.

Problem

• Debiased inference on differentially private data
• Address clamping bias in parametric bootstrap
• Improve confidence intervals and hypothesis tests accuracy

Innovation

• Debiased parametric bootstrap for private data
• Indirect inference to handle clamping effects
• Adaptive estimator minimizes asymptotic variance