Estimating high-dimensional directed acyclic graphs with the PC-algorithm
Abstract
We consider the PC-algorithm Spirtes et. al. (2000) for estimating the skeleton of a very high-dimensional acyclic directed graph (DAG) with corresponding Gaussian distribution. The PC-algorithm is computationally feasible for sparse problems with many nodes, i.e. 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 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<infinity. The sparseness assumption is rather minimal requiring only that the neighborhoods in the DAG are of lower order than sample size n. We empirically demonstrate the PC-algorithm for simulated data and argue that the algorithm is rather insensitive to the choice of its single tuning parameter.
Cite
@article{arxiv.math/0510436,
title = {Estimating high-dimensional directed acyclic graphs with the PC-algorithm},
author = {Markus Kalisch and Peter Buehlmann},
journal= {arXiv preprint arXiv:math/0510436},
year = {2007}
}