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ICML
2006
IEEE

Convex optimization techniques for fitting sparse Gaussian graphical models

10 years 6 months ago
Convex optimization techniques for fitting sparse Gaussian graphical models
We consider the problem of fitting a large-scale covariance matrix to multivariate Gaussian data in such a way that the inverse is sparse, thus providing model selection. Beginning with a dense empirical covariance matrix, we solve a maximum likelihood problem with an l1-norm penalty term added to encourage sparsity in the inverse. For models with tens of nodes, the resulting problem can be solved using standard interior-point algorithms for convex optimization, but these methods scale poorly with problem size. We present two new algorithms aimed at solving problems with a thousand nodes. The first, based on Nesterov's first-order algorithm, yields a rigorous complexity estimate for the problem, with a much better dependence on problem size than interior-point methods. Our second algorithm uses block coordinate descent, updating row/columns of the covariance matrix sequentially. Experiments with genomic data show that our method is able to uncover biologically interpretable conne...
Onureena Banerjee, Laurent El Ghaoui, Alexandre d'
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2006
Where ICML
Authors Onureena Banerjee, Laurent El Ghaoui, Alexandre d'Aspremont, Georges Natsoulis
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