Sparse permutation invariant covariance estimation

Adam J. Rothman, Peter J. Bickel, Elizaveta Levina, Ji Zhu

Research output: Contribution to journalArticlepeer-review

445 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)494-515
Number of pages22
JournalElectronic Journal of Statistics
Volume2
DOIs
StatePublished - 2008

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