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Estimating high-dimensional directed acyclic graphs with the PC-algorithm

2005; Cornell University; Linguagem: Inglês

10.48550/arxiv.math/0510436

Markus Kalisch, Peter Bühlmann,

Statistical Methods and Inference

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