Efficient estimation of covariance selection models

By Frederic Wong, Chris Carter, Robert Kohn. 2003

215 citations recorded by the source corpus.

A Bayesian method is proposed for estimating an inverse covariance matrix from Gaussian data. The method is based on a prior that allows the off-diagonal elements of the inverse covariance matrix to be zero, and in many applications results in a parsimonious parameterisation of the covariance matrix. No assumption is made about the structure of the corresponding graphical model, so the method applies to both nondecomposable and decomposable graphs. All the parameters are estimated by model averaging using an efficient Metropolis--Hastings sampling scheme. A simulation study demonstrates that the method produces statistically efficient estimators of the covariance matrix, when the inverse covariance matrix is sparse. The methodology is illustrated by applying it to three examples that are high-dimensional relative to the sample size. Copyright Biometrika Trust 2003, Oxford University Press.

Subfields: Artificial Intelligence, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/dfb27ed98bb2c8f927b6e07a272460f08167c133

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Citations in the corpus

Covariance matrix selection and estimation via penalised normal likelihood (2006, methodology): “Many existing methods deal directly with the individual elements of the covariance matrix; for a review of some of these methods see Diggle & Verbyla (1998), Diggle et al. (2002), Boik (2002) and Wong et al. (2003) .”
High dimensional covariance matrix estimation using a factor model (2007, unknown): “Smith and Kohn (2002), Wong, Carter and Kohn (2003) , Wu and Pourahmadi (2003),”
An empirical Bayes approach to inferring large-scale gene association networks (2005, methodology): “Motivated by these challenges, great efforts are now being undertaken to further extend the theory of graphical models to allow their large-scale application on small-sample data (e.g., Wong et al., 2003; Dobra et al., 2004).”
MCMC Estimation of Restricted Covariance Matrices (2009, methodology): “…the components of a correlation matrix has been implemented in Gaussian copula models by Pitt, Chan, and Kohn (2006) using the parameterization of Wong, Carter, and Kohn (2003), and in hierarchical shrinkage models by Barnard, McCulloch, and Meng (2000) using the griddy Gibbs sampler (Ritter and…”
Bayesian inference for multivariate copulas using pair-copula constructions. (2010, methodology): “Pitt et al. (2006) solved by employing covariance selection prior of Wong et al. (2003).”
Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “2003) and Gaussian graphical models (Wong et al. 2003 ; Meinshausen and Bühlmann, 2006; Yuan and Lin, 2007).”