Efficient Covariance Approximations for Large Sparse Precision Matrices
Journal article, 2018

Published with license by Taylor & Francis Group, LLC. The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be nontrivial to obtain when the dimension is large. This article introduces a fast Rao–Blackwellized Monte Carlo sampling-based method for efficiently approximating selected elements of the covariance matrix. The variance and confidence bounds of the approximations can be precisely estimated without additional computational costs. Furthermore, a method that iterates over subdomains is introduced, and is shown to additionally reduce the approximation errors to practically negligible levels in an application on functional magnetic resonance imaging data. Both methods have low memory requirements, which is typically the bottleneck for competing direct methods.

Gaussian Markov random fields

Sparse precision matrix

Stochastic approximation

Selected inversion

Spatial analysis


Per Sidén

Linköping University

Finn Lindgren

University of Edinburgh

David Bolin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mattias Villani

Linköping University

Journal of Computational and Graphical Statistics

1061-8600 (ISSN) 1537-2715 (eISSN)

Vol. 27 4 898-909

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Signal Processing



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