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Differential privacy is a popular privacy-enhancing technology that has been deployed both by industry and government agencies. Unfortunately, existing explanations of differential privacy fail to set accurate privacy expectations for data subjects, which depend on the choice of deployment model. We design and evaluate new explanations of differential privacy for the local and central models, drawing inspiration from prior work explaining other privacy-enhancing technologies such as encryption. We reflect on the challenges in evaluating explanations and on the tradeoffs between qualitative and quantitative evaluation strategies. These reflections offer guidance for other researchers seeking to design and evaluate explanations of privacy-enhancing technologies. 

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 provide the first algorithms for differentially private synthetic control with explicit error bounds. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We provide upper and lower bounds on the sensitivity of the synthetic control query and provide explicit error bounds on the accuracy of our private synthetic control algorithms. We show that our algorithms produce accurate predictions for the target unit and that the cost of privacy is small. Finally, we empirically evaluate the performance of our algorithm, and show favorable performance in a variety of parameter regimes, as well as provide guidance to practitioners for hyperparameter tuning.