Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix
提出一种基于样本协方差矩阵平方根的简单改进方法，在不显著增加计算成本的前提下提升图形套索估计精度矩阵的统计性能，并通过模拟和真实数据验证其有效性。
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 eigenvalues. 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.