Model Agnostic Differentially Private Causal Inference

TL;DR

This work tackles the challenge of estimating population-level causal effects from observational data under formal privacy guarantees. It introduces a model-agnostic DP framework that decouples nuisance-function estimation from privacy by using fold-based data splitting and ensemble aggregation, privatizing only the final ATE estimate and its variance under GDP. The authors instantiate the framework for the G-formula, IPW, and AIPW estimators, derive unified privacy–utility guarantees, and extend to meta-analysis of multiple private ATEs. Empirical results on synthetic data show competitive performance across realistic privacy budgets, with robust behavior under model misspecification and varying overlap, highlighting the practical impact for privacy-preserving causal inference in real-world datasets.

Abstract

Estimating causal effects from observational data is essential in fields such as medicine, economics and social sciences, where privacy concerns are paramount. We propose a general, model-agnostic framework for differentially private estimation of average treatment effects (ATE) that avoids strong structural assumptions on the data-generating process or the models used to estimate propensity scores and conditional outcomes. In contrast to prior work, which enforces differential privacy by directly privatizing these nuisance components and results in a privacy cost that scales with model complexity, our approach decouples nuisance estimation from privacy protection. This separation allows the use of flexible, state-of-the-art black-box models, while differential privacy is achieved by perturbing only predictions and aggregation steps within a fold-splitting scheme with ensemble techniques. We instantiate the framework for three classical estimators -- the G-formula, inverse propensity weighting (IPW), and augmented IPW (AIPW) -- and provide formal utility and privacy guarantees. Empirical results show that our methods maintain competitive performance under realistic privacy budgets. We further extend our framework to support meta-analysis of multiple private ATE estimates. Our results bridge a critical gap between causal inference and privacy-preserving data analysis.

Figures (4)

• Figure 1: The left plot depicts a well-specified setting with low overlap. The right plot shows a setting where misspecified estimators have large bias.
• Figure 2: Well-specified setting with good overlap: propensity scores and outcome are linear models.
• Figure 3: Effect of changing $K$ for G-formula linear regression. The aggregated estimators perform well even as $K$ increases. Although the nuisance estimators are each trained on smaller folds which increases variance this is balanced by aggregating more estimators. However, at $K=400$ the performance of the aggregator estimator degrades as each fold contains only $50$ samples.
• Figure 4: Effect of changing $K$ for IPW and AIPW. We see that in this setup the accuracy of IPW quickly decreases. In contrast, AIPW benefits from the performance of G-formula and remains stable for moderate values of $K$.

Theorems & Definitions (25)

• Definition 1: Average Treatment Effect (ATE)
• Definition 2: Trade-off function
• Definition 3: $\zeta$-Gaussian Differential Privacy Dong22GDP
• Lemma 1: Gaussian mechanism Dong22GDP
• Remark 1: Data splitting and connections to existing techniques
• Theorem 1: Privacy analysis
• Theorem 2: Utility analysis
• proof
• Remark 2: Model sensitivity
• Proposition 1