Open Access
2009 High dimensional sparse covariance estimation via directed acyclic graphs
Philipp Rütimann, Peter Bühlmann
Electron. J. Statist. 3: 1133-1160 (2009). DOI: 10.1214/09-EJS534


We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian distribution based on a DAG. For inferring the underlying DAG we use the PC-algorithm [27] and for estimating the DAG-based covariance matrix and its inverse, we use a Cholesky decomposition approach which provides a positive (semi-)definite sparse estimate. We present a consistency result in the high-dimensional framework and we compare our method with the Glasso [12, 8, 2] for simulated and real data.


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Philipp Rütimann. Peter Bühlmann. "High dimensional sparse covariance estimation via directed acyclic graphs." Electron. J. Statist. 3 1133 - 1160, 2009.


Published: 2009
First available in Project Euclid: 1 December 2009

zbMATH: 1326.62124
MathSciNet: MR2566184
Digital Object Identifier: 10.1214/09-EJS534

Primary: 62H12
Secondary: 62F12

Keywords: concentration matrix , Covariance matrix , directed acyclic graphs , graphical lasso , High-dimensional data , PC-algorithm

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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