Exact covariance thresholding into connected components for large-scale Graphical Lasso

Rahul Mazumder; Trevor Hastie

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arXiv · 1108.3829

Exact covariance thresholding into connected components for large-scale Graphical Lasso

Rahul Mazumder·Trevor Hastie

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Abstract

We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter $\rho$. Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at $\rho$ is decomposed into connected components. We show that the vertex-partition induced by the thresholded covariance graph is exactly equal to that induced by the estimated concentration graph. This simple rule, when used as a wrapper around existing algorithms, leads to enormous performance gains. For large values of $\rho$, our proposal splits a large graphical lasso problem into smaller tractable problems, making it possible to solve an otherwise infeasible large scale graphical lasso problem.

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Rahul Mazumder, Trevor Hastie. 2011-08-18. Exact covariance thresholding into connected components for large-scale Graphical Lasso. https://arxiv.org/abs/1108.3829

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