2008/01/01 by Adam J. Rothman, Peter J. Bickel, Elizaveta Levina +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Gene expression and cancer classification #Single-cell and spatial transcriptomics #Statistical Methods and Inference #math.ST #msc:62H12 #msc:62H20 #stat.TH
paper · pdf · doi:10.1214/08-ejs176
published as Electronic Journal of Statistics 2008, Vol. 2, 494-515 · Published in at http://dx.doi.org/10.1214/08-EJS176 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/01/01 · arxiv created 2008/06/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.