Research map / Federated learning and privacy / Differential privacy
Analysis of Differentially Private Synthetic Data: A Measurement Error Approach
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Connects Gaussian-mechanism differentially private synthetic data to classical measurement error models to derive MLE-based bias-corrected DP estimators and valid asymptotic confidence intervals for linear regression coefficients.
Problem
Statistical inference (unbiased point estimates and valid confidence intervals) from differentially private synthetic datasets is under-explored; naive analyses ignoring DP noise yield biased estimates and invalid CIs.
Approach
Treat the analytic Gaussian mechanism output on the dataset as a classical additive measurement error model with known error variance, then apply measurement-error theory (Fuller 1987) to get a bias-corrected estimator and a sandwich-style asymptotic variance and CI for linear regression coefficients.
Key results
- Naive CIs ignoring DP noise never capture the true beta_1 in simulations, while the proposed asymptotic CIs achieve coverage close to the nominal 90% level.
- The proposed estimator is generally less accurate than SSP at small sample sizes or moderate privacy budgets, but becomes comparable when epsilon is small with small n or when both epsilon and n are large (e.g., MAE 0.128 vs 0.128 at n=1e5 for Gaussian).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed Gaussian-mechanism measurement-error estimator instead of SSP | Linear regression coefficient estimation · Gaussian and uniform predictors across reported sample sizes and privacy budgets | MAE | Mixed |
| Account for DP noise when constructing the confidence interval rather than using the naive CI that ignores it | Proposed estimator on the synthetic dataset · Gaussian and uniform predictor simulations | coverage | Helped |
| Increase the privacy budget ε | Proposed estimator · Linear regression simulations across reported sample sizes | MAE | Helped |
| Increase sample size n | Proposed estimator · Linear regression simulations across reported privacy budgets | MAE | Helped |
Surprising findings
- When privacy budget is small, the naive estimator can have smaller variance than the true-data estimator yet be biased, so its CI is precise but wrong.
- The proposed estimator is often outperformed by SSP in MAE at moderate sample sizes and privacy budgets.
Limitations
- Restricted to linear regression with additive Gaussian noise and Gaussian covariates; nonlinear models such as logistic regression left for future work.
- Clipping to ensure finite sensitivity invalidates the asymptotic theorem unless the clipping interval is large; the finite-sample estimator performs poorly when noise is large relative to sample size.
Experimental setup
Datasets: simulated linear regression data (Gaussian and uniform covariates)
Benchmarks: simulation study with n from 500 to 1e5 and epsilon in {0.1,0.5,1,5}
Metrics: median absolute error coverage probability of 90% confidence intervals margin of error
Baselines: sufficient statistic perturbation (SSP) naive CI ignoring DP noise
Builds on: analytic Gaussian mechanism measurement error theory (Fuller 1987) sufficient statistic perturbation
Closest papers by meaning
- Debiasing Synthetic Data Generated by Deep Generative Models (NeurIPS 2024 · similarity 0.88)
- Private Evolution Converges (NeurIPS 2025 · similarity 0.87)
- Optimal Differentially Private Model Training with Public Data (ICML 2024 · similarity 0.87)
- Differentially Private Synthetic Data via Foundation Model APIs 1: Images (ICLR 2024 · similarity 0.87)
- Private Statistical Estimation via Truncation (NeurIPS 2025 · similarity 0.87)
- Bounding the Excess Risk for Linear Models Trained on Marginal-Preserving, Differentially-Private, Synthetic Data (ICML 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.