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arXiv · 0911.2375

High dimensional sparse covariance estimation via directed acyclic graphs

Philipp Rütimann·Peter Bühlmann
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Abstract

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 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 for simulated and real data.

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Philipp Rütimann, Peter Bühlmann. 2009-11-17. High dimensional sparse covariance estimation via directed acyclic graphs. https://doi.org/10.1214/09-ejs534

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