an:07061492
Zbl 1414.62224
Avagyan, Vahe; Alonso, Andr??s M.; Nogales, Francisco J.
D-trace estimation of a precision matrix using adaptive lasso penalties
EN
Adv. Data Anal. Classif., ADAC 12, No. 2, 425-447 (2018).
00411392
2018
j
62H30 62J10 65S05
adaptive thresholding; D-trace loss; Gaussian graphical model; gene expression data; high-dimensionality
Summary: The accurate estimation of a precision matrix plays a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the \(\ell_1\) norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimate for properly selected penalty parameters. However, the \(\ell_1\) norm penalization often fails to control the bias of obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed \(\ell_1\) norm penalized D-trace loss minimization method. They aim at reducing the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators.