Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm
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(na) for any 0 a n. We also demonstrate the PC-algorithm for simulated data.
Cite
Text
Kalisch and Bühlmann. "Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm." Journal of Machine Learning Research, 2007.Markdown
[Kalisch and Bühlmann. "Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm." Journal of Machine Learning Research, 2007.](https://mlanthology.org/jmlr/2007/kalisch2007jmlr-estimating/)BibTeX
@article{kalisch2007jmlr-estimating,
title = {{Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm}},
author = {Kalisch, Markus and Bühlmann, Peter},
journal = {Journal of Machine Learning Research},
year = {2007},
pages = {613-636},
volume = {8},
url = {https://mlanthology.org/jmlr/2007/kalisch2007jmlr-estimating/}
}