Differential Privacy Preserving Causal Graph Discovery

Discovering causal relationships by constructing the causal graph provides critical information to researchers and decision makers. Yet releasing causal graphs may risk leakage of individual participant's privacy. It is very underexploited how to enforce differential privacy in causal graph discovery. In this work, we focus on the PC algorithm, a classic constraint-based causal graph discovery algorithm, and propose a differentially private PC algorithm (PrivPC) for categorical data. PrivPC adopts the exponential mechanism and significantly reduces the number of edge elimination decisions. Therefore, it incurs much less privacy budget than the naive approaches that add privacy protection at each conditional independence test. For numerical data, we further develop a differentially private causal discovery algorithm (PrivPC*). The idea is to add noise once onto the covariance matrix from which partial correlations used for conditional independence test can be derived. Experimental results show that PrivPC and PrivPC* achieve good utility and robustness for different settings of causal graphs. To our best knowledge, this is the first work on how to enforce differential privacy in constraint-based causal graph discovery.