Causal graph discovery refers to the process of discovering causal relation graphs from purely observational data. Like other statistical data, a causal graph might leak sensitive information about participants in the dataset. In this paper, we present a differentially private causal graph discovery algorithm, Priv-PC, which improves both utility and running time compared to the state-of-the-art. The design of Priv-PC follows a novel paradigm called sieve-and-examine which uses a small amount of privacy budget to filter out "insignificant" queries, and leverages the remaining budget to obtain highly accurate answers for the "significant" queries. We also conducted the first sensitivity analysis for conditional independence tests including conditional Kendall's tau and conditional Spearman's rho. We evaluated Priv-PC on 4 public datasets and compared with the state-of-the-art. The results show that Priv-PC achieves 10.61 to 32.85 times speedup and better utility.
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