Differentially Private Covariate Balancing Causal Inference

Workload-based differentially private (DP) synthetic data methods privately measure aggregate queries and post-process the noisy answers into synthetic records. Generic workloads can achieve strong distributional fidelity, but causal estimands such as the average treatment effect (ATE) depend on treatment-arm balance and outcome moments that generic marginals need not preserve. We propose causal workloads: DP query sets designed around the orthogonal moments used by doubly robust causal estimators. The released workload can be used directly by stable moment-map estimators or reconstructed by maximum-entropy calibration into reusable synthetic data; our theory decomposes ATE error into sampling, privacy, workload-approximation, Monte Carlo, and calibration terms. We also introduce Causal-AIM, an adaptive workload selector, and a noise-aware multiple-imputation (NA+MI) procedure for confidence intervals from DP synthetic data. Because the workload is released once, the same DP synthetic table can support ATE, ATT, and subgroup analyses without additional privacy spending. Empirically, causal workloads are most useful at strict privacy budgets and for calibrated uncertainty, while generic workloads often retain an advantage for point RMSE as privacy relaxes. The broader lesson is a tradeoff: distributional fidelity can help point accuracy, but valid causal inference requires preserving causal moments and propagating DP noise rather than treating synthetic rows as real.

Average treatment effect (ATE) estimation in observational studies is a fundamental statistical tool used frequently in social science, medicine, and other fields. These fields often work with sensitive data where privacy protections are important, so a differentially private mechanism for ATE estimation is highly desirable. Here we present two propensity score-based algorithms for ATE estimation on observational data, one improving the inverse probability weighting (IPW) method used in prior work, and the other using blocking on the propensity score (BPS). Both show lower error and less bias than prior work, with the BPS-based algorithm frequently reducing error by 75% or more compared to prior work.

We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This applies in the natural setting where the modeler supplies separate bounds for each variable, so that individual entries can be measured with less noise than the full matrix. In each round, our method selects a poorly approximated entry, measures it using the Gaussian mechanism, and then reconstructs a full covariance matrix using a maximum-entropy reconstruction objective, leading to a Gaussian graphical model structure. Experiments on diverse real-world datasets demonstrate consistent improvements in estimation error with respect to the Gaussian mechanism and other baselines, particularly in high-dimensional and low-to-moderate privacy regimes.