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Efficient Covariance Approximations for Large Sparse Precision Matrices
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
Univ Edinburgh, Scotland.
Chalmers and Univ Gothenburg, Sweden.
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
2018 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 4, p. 898-909Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
AMER STATISTICAL ASSOC , 2018. Vol. 27, no 4, p. 898-909
Keywords [en]
Gaussian Markov random fields; Selected inversion; Sparse precision matrix; Spatial analysis; Stochastic approximation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-153715DOI: 10.1080/10618600.2018.1473782ISI: 000453029500018OAI: oai:DiVA.org:liu-153715DiVA, id: diva2:1276178
Note

Funding Agencies|Swedish Research Council (Vetenskapsradet) [2013-5229, 2016-04187]; European Unions Horizon 2020 Programme for Research and Innovation [640171]

Available from: 2019-01-07 Created: 2019-01-07 Last updated: 2019-03-25

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Citation style
  • apa
  • harvard1
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