Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix Articles uri icon

publication date

  • October 2017

start page

  • 865

end page

  • 872

issue

  • 4

volume

  • 26

international standard serial number (ISSN)

  • 1061-8600

electronic international standard serial number (EISSN)

  • 1537-2715

abstract

  • In this article, we focus on the estimation of a high-dimensional inverse covariance (i.e., precision) matrix. We propose a simple improvement of the graphical Lasso (glasso) framework that is able to attain better statistical performance without increasing significantly the computational cost. The proposed improvement is based on computing a root of the sample covariance matrix to reduce the spread of the associated eigen values. Through extensive numerical results, using both simulated and real datasets, we show that the proposed modification improves the glasso procedure. Our results reveal that the square-root improvement can be a reasonable choice in practice. Supplementary material for this article is available online.

keywords

  • gaussian graphical model; gene expression; high-dimensionality; penalized estimation; portfolio selection