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dc.contributor.author
Kalisch, Markus
dc.contributor.author
Bühlmann, Peter Lukas
dc.date.accessioned
2017-06-09T19:45:08Z
dc.date.available
2017-06-09T19:45:08Z
dc.date.issued
2005
dc.identifier.uri
http://hdl.handle.net/20.500.11850/46794
dc.description.abstract
We consider the PC-algorithm ([13]) for estimating the skeleton of a very highdimensional 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(na) for any 0 < a < 1. 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.language.iso
en
dc.publisher
Seminar für Statistik, Eidgenössische Technische Hochschule (ETH)
dc.title
Estimating high-dimensional directed acyclic graphs with the PC-algorithm
dc.type
Report
ethz.journal.title
Research report
ethz.journal.volume
130
ethz.size
17 p.
ethz.notes
.
ethz.identifier.nebis
005073761
ethz.publication.place
Zürich
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)::03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)::03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
ethz.identifier.url
ftp://ftp.stat.math.ethz.ch/Research-Reports/130.pdf
ethz.date.deposited
2017-06-09T19:47:22Z
ethz.source
ECIT
ethz.identifier.importid
imp59364f0648a6146141
ethz.ecitpid
pub:76885
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-12T20:25:31Z
ethz.rosetta.lastUpdated
2018-10-01T16:17:30Z
ethz.rosetta.versionExported
true
ethz.COinS
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