Home Page




Editorial Board

Special Issues

Open Source Software

Proceedings (PMLR)

Data (DMLR)

Transactions (TMLR)




Frequently Asked Questions

Contact Us

RSS Feed

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

Markus Kalisch, Peter B├╝hlmann; 8(22):613−636, 2007.


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(na) for any 0 < a < ∞. The sparseness assumption is rather minimal requiring only that the neighborhoods in the DAG are of lower order than sample size n. We also demonstrate the PC-algorithm for simulated data.

© JMLR 2007. (edit, beta)