Locally Private Causal Inference

Local differential privacy (LDP) is a differential privacy (DP) paradigm in which individuals transmit their data to a curator after applying a DP mechanism to it (often by adding noise). LDP ensures more stringent user privacy protection because the curator does not have access to any of the user's original information. On the curator's side, however, the noise for privacy results in additional bias and variance in their analyses, thus it is of great interest for analysts to understand how noise impacts their analyses and to conduct informative analyses. In this article, we develop statistically valid methodologies to infer causal effects from the privatized data under the Rubin Causal Model framework. First, we present asymptotically unbiased and consistent estimators with their variance estimators and plug-in confidence intervals. Second, we develop a Bayesian nonparametric methodology, which performs well in terms of MSE for tight privacy budgets. A blocked Gibbs sampling algorithm has been developed. Finally, we present simulation studies to evaluate the performance of frequentist and Bayesian methodologies for various privacy budgets, resulting in useful suggestions for performing causal inference for differentially private data.