Year: 2011
Type: preprint
Abstract: We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter $ρ$. Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at $ρ$ 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 $ρ$, 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.
Source: arXiv (Cornell University)
Authors: Mazumder, Rahul, Hastie, Trevor
Institution: Stanford University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950215113