High dimensional sparse covariance estimation via directed acyclic graphs

Abstract

We present a graph-based technique for estimating sparse covariancematrices and their inverses from high-dimensionaldata. Themethod 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 covariancematrix 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. © 2009, Institute of Mathematical Statistics. All rights reserved.