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High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence

2011
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Electronic Journal of Statistics
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Given i.i.d. observations of a random vector X ∈ R p , we study the problem of estimating both its covariance matrix Σ * , and its inverse covariance or concentration matrix Θ * = (Σ * ) −1 . When X is multivariate Gaussian, the non-zero structure of Θ * is specified by the graph of an associated Gaussian Markov random field; and a popular estimator for such sparse Θ * is the ℓ 1 -regularized Gaussian MLE. This estimator is sensible even for for non-Gaussian X, since it corresponds to

doi:10.1214/11-ejs631
fatcat:cclcuirfrrb4tfub5m72smas2e