文章基本信息

标题：Graphical-model based high dimensional generalized linear models
本地全文：下载
作者：Yaguang Li ; Wei Xu ; Xin Gao 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：1
页码：1993-2028
DOI：10.1214/21-EJS1831
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of both prediction and model selection in high dimensional generalized linear models. Predictive performance can be improved by leveraging structure information among predictors. In this paper, a graphic model-based doubly sparse regularized estimator is discussed under the high dimensional generalized linear models, that utilizes the graph structure among the predictors. The graphic information among predictors is incorporated node-by-node using a decomposed representation and the sparsity is encouraged both within and between the decomposed components. We propose an efficient iterative proximal algorithm to solve the optimization problem. Statistical convergence rates and selection consistency for the doubly sparse regularized estimator are established in the ultra-high dimensional setting. Specifically, we allow the dimensionality grows exponentially with the sample size. We compare the estimator with existing methods through numerical analysis on both simulation study and a microbiome data analysis.
关键词：62F12; 62J07; 62J12; Model selection; proximal operator; random design; regularization; statistical consistency; undirected graph