多图模型及其在宏观经济指标相关分析中的应用

多图模型表示来自于不同类的同一组随机变量间的相关关系,结点表示随机变量,边表示变量之间的直接联系,各类的图模型反映了各自相关结构特征和类间共同的信息。用多图模型联合估计方法,将来自不同个体的数据按其特征分类,假设每类中各变量间的相依结构服从同一个高斯图模型,应用组Lasso方法和图Lasso方法联合估计每类的图模型结构。数值模拟验证了多图模型联合估计方法的有效性。用多图模型和联合估计方法对中国15个省份13个宏观经济指标进行相依结构分析,结果表明,不同经济发展水平省份的宏观经济变量间存在共同的相关联系,反映了中国现阶段经济发展的特征;每一类的相关结构反映了各类省份经济发展独有的特征。

Multiple Graphical Models with Application to Correlation Analysis of Macroeconomic Index

The dependence structure of variables from different groups is expressed by multiple graphical models.The vertices representing the variables,are connected by undirected edges according to the relations between the variables.Graphical models of different groups represent the individual and common features between groups.The joint estimation methods of multiple Gaussian graphical models are proposed,assuming the variables from the same group have the same graphical models.Group Lasso and graphical Lasso are used to learn the graphical models of every group.The validity of the proposed method is confirmed by simulations.At last,the method is applied to the Macroeconomic Index of 13 variables from 15 provinces.Empirical results show that the dependent structures of provinces with different economic development level are different,simultaneously with the common features of the multiple graphical models.