Differentially Private Synthetic Control

Abstract

Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we suggest the first algorithms for differentially private synthetic control with explicit error bounds based on the analysis of the sensitivity of the synthetic control query. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We empirically evaluate the performance of our algorithms and show favorable results in a variety of parameter regimes.