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2008 Sparse permutation invariant covariance estimation
Adam J. Rothman, Peter J. Bickel, Elizaveta Levina, Ji Zhu
Electron. J. Statist. 2: 494-515 (2008). DOI: 10.1214/08-EJS176


The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension p and sample size n are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data.


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Adam J. Rothman. Peter J. Bickel. Elizaveta Levina. Ji Zhu. "Sparse permutation invariant covariance estimation." Electron. J. Statist. 2 494 - 515, 2008.


Published: 2008
First available in Project Euclid: 26 June 2008

zbMATH: 1320.62135
MathSciNet: MR2417391
Digital Object Identifier: 10.1214/08-EJS176

Primary: 62H20
Secondary: 62H12

Keywords: Cholesky decomposition , Covariance matrix , high dimension low sample size , large p small n , Lasso , Sparsity

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society


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