Estimating high-dimensional directed acyclic graphs with the pc-algorithm (2005)
| Venue: | Journal of Machine Learning Research |
| Citations: | 31 - 4 self |
BibTeX
@TECHREPORT{Kalisch05estimatinghigh-dimensional,
author = {Markus Kalisch and Peter Bühlmann and Maxwell Chickering},
title = {Estimating high-dimensional directed acyclic graphs with the pc-algorithm},
institution = {Journal of Machine Learning Research},
year = {2005}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
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 < 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. Keywords: asymptotic consistency, DAG, graphical model, PC-algorithm, skeleton 1.
