具有协变量的高斯图模型的结构学习  

Structure Learning of Gaussian Graphical Model with Covariates

作　　者：马燕 张海 MA Yan;ZHANG Hai(School of Mathematics,Northwest University,Xi'an 710069)

机构地区：[1]西北大学数学学院,西安710069

出　　处：《工程数学学报》2018年第5期489-501,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11571011)~~

摘　　要：图模型是一种研究变量之间相依关系的重要工具.除了节点变量外,数据常常包括协变量而且可能影响网络结构.然而现有关于图模型的工作大多仅考虑节点变量.本文基于图模型研究具有协变量的网络结构特征学习问题,在稀疏正则化的框架下,通过假设变量之间的条件独立为线性关系,建立具有协变量信息的稀疏高斯图模型,估计网络结构特征.所得结果具有实际解释性且易于求解,我们利用坐标下降法求解模型,通过实验说明含协变量比无协变量的效果更好,从而说明本文模型的高效性和实用性.Graphical models is an important tool to study the relationship among variables.Besides the node variables,the additional covariates are frequently recorded together with the data and may influence the dependence relationships.However,most of the existing work on graphical models only considers the node variables.In this paper,we study the problem of reconstructing network structure from the data with covariates by applying the tools of graphical models.In the framework of sparse regularization,we propose a novel sparse Gaussian graphical models to incorporate the covariates information,where the conditional independency relationship between variables are assumed to be a linear function of the covariates.The proposed model is interpretable and easy to solve.We employ the coordinate descent algorithm to solve the model.A series of numerical examples shows that the effect of the covariate is better than that of the non covariate,which indicates the effectiveness and efficiency of the proposed model.

关 键 词：图模型 稀疏 正则化 协变量 SCAD 

分 类 号：O212[理学—概率论与数理统计]