Estimating high-dimensional directed acyclic graphs with the PC-algorithm
| dc.creator | Kalisch, Markus | |
| dc.creator | Buehlmann, Peter | |
| dc.date | 2005-10-20 | |
| dc.date.accessioned | 2026-07-07T08:07:20Z | |
| dc.date.available | 2026-07-07T08:07:20Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0510436 | |
| dc.identifier | http://arxiv.org/abs/math/0510436 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130909 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62H20, 62H12 (Primary), 68Q32 (Secondary) | |
| dc.title | Estimating high-dimensional directed acyclic graphs with the PC-algorithm | |
| dc.type | text |