Causal Structure Learning with Reduced Partial Correlation Thresholding

Abstract

Directed acyclic graphs (DAGs) are commonly used to represent causal relations within a large number of random variables. Estimating DAGs from observational data is a difficult task, it is often impossible to uniquely determine edge direction. The skeleton of the graph, where directions are removed from edges, is often estimated instead. We consider the task of estimating the skeleton of a potentially high-dimensional DAG consisting of Gaussian random variables. A drawback of existing methods is that a prohibitively large number of conditional independence relations need to be tested for. By exploiting properties of common random graph families, we develop a new algorithm that requires conditioning only on small sets of variables. By extending previous theoretical results for undirected graphs to the setting of directed graphs, we prove the consistency of our algorithm, and demonstrate improvements over the state-of-the-art alternative in low and high-dimensional simulation settings. We conclude by applying our proposed algorithm on a real gene expression data set.