Description
Smooth L0 Penalty Approximations for Gaussian Graphical Models.
Description
Provides smooth approximations to the L0 norm penalty for estimating sparse Gaussian graphical models (GGMs). Network estimation is performed using the Local Linear Approximation (LLA) framework (Fan & Li, 2001 <doi:10.1198/016214501753382273>; Zou & Li, 2008 <doi:10.1214/009053607000000802>) with five penalty functions: arctangent (Wang & Zhu, 2016 <doi:10.1155/2016/6495417>), EXP (Wang, Fan, & Zhu, 2018 <doi:10.1007/s10463-016-0588-3>), Gumbel, Log (Candes, Wakin, & Boyd, 2008 <doi:10.1007/s00041-008-9045-x>), and Weibull. Adaptive penalty parameters for EXP, Gumbel, and Weibull are estimated via maximum likelihood, and model selection uses information criteria including AIC, BIC, and EBIC (Extended BIC). Simulation functions generate multivariate normal data from GGMs with stochastic block model or small-world (Watts-Strogatz) network structures.