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Fitting very large sparse Gaussian graphical models

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  • Kiiveri, Harri
  • de Hoog, Frank

Abstract

In this paper we consider some methods for the maximum likelihood estimation of sparse Gaussian graphical (covariance selection) models when the number of variables is very large (tens of thousands or more). We present a procedure for determining the pattern of zeros in the model and we discuss the use of limited memory quasi-Newton algorithms and truncated Newton algorithms to fit the model by maximum likelihood. We present efficient ways of computing the gradients and likelihood function values for such models suitable for a desktop computer. For the truncated Newton method we also present an efficient way of computing the action of the Hessian matrix on an arbitrary vector which does not require the computation and storage of the Hessian matrix. The methods are illustrated and compared on simulated data and applied to a real microarray data set.

Suggested Citation

  • Kiiveri, Harri & de Hoog, Frank, 2012. "Fitting very large sparse Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2626-2636.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2626-2636
    DOI: 10.1016/j.csda.2012.02.007
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Søren Højsgaard & Steffen L. Lauritzen, 2008. "Graphical Gaussian models with edge and vertex symmetries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 1005-1027, November.
    4. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
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    Cited by:

    1. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.

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