Title

Differential Privacy Preserving Causal Graph Discovery

Document Type

Article

Publication Date

2017

Keywords

Privacy, Skeleton, Correlation, Markov processes, Data privacy, Probability distribution, Electronic mail, belief networks, causality, data mining, data privacy, graph theory, privacy budget, privacy protection, conditional independence test, differentially private causal discovery algorithm, differential privacy preserving causal graph discovery, causal relationships, individual participant, causal graph discovery algorithm, differentially private PC algorithm, PrivPC, categorical data, exponential mechanism, edge elimination decisions, covariance matrix, constraint-based causal graph discovery, differential privacy, causal graph, PC algorithm

Abstract

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.

Comments

Principal Investigator: Xintao Wu

Acknowledgements: This work was supported in part to Depeng Xu and Xintao Wu by U.S. National Institute of Health (1R01GM103309) and National Science Foundation (DGE-1523115 and IIS-1502273) and to Shuhan Yuan by China Scholarship Council. This research was conducted while Shuhan Yuan visited University of Arkansas.

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