Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm

We consider the PC-algorithm (Spirtes et al., 2000) for estimating the skeleton and equivalence class of a very high-dimensional directed acyclic graph (DAG) with corresponding Gaussian distribution. The PC-algorithm is computationally feasible and often very fast for sparse problems with many nodes (variables), and it has the attractive property to automatically achieve high computational efficiency as a function of sparseness of the true underlying DAG. We prove uniform consistency of the algorithm for very high-dimensional, sparse DAGs where the number of nodes is allowed to quickly grow with sample size n, as fast as O ( n a ) for any 0 [abs] [ pdf ][ bib ] &copy JMLR 2007. ( edit, beta )

Authors

• Markus Kalisch
• Peter Bühlmann

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