结构VAR模型辨识的条件互信息图模型

Identification of Structure VAR Models Using Conditional Mutual Information Graphs

在结构向量自回归(VAR)模型辨识的图模型中引入信息论方法.定义了线性条件互信息图,图中的结点表示时间序列不同时刻的随机变量,结点间的边表示随机变量之间存在的因果相依关系.提出了随机变量之间条件线性联系存在性的信息论检验方法.图中边的存在性用基于线性条件互信息的枢轴量检验,枢轴量的显著性用置换检验决定.用统计分析的方法确定当前变量之间联系的方向,建立了有向非循环图.最后以模拟序列为例,验证了所提出的方法是可行且有效的.

A class graphical models, called linear conditional mutual information graph, is proposed for identification structural vector autoregression model. The vertex set denotes random variables at different times, and the directed edges denote causal dependence between the variables. The presence of the edges is tested by a statistics based on linear conditional mutual information. The permutation procedure is used to determine the significance of the test statistics. The direction of the relationships of the current variables is determined by a statistical method and lead to directed acyclic graph. The method is demonstrated by simulation time series with different dependence structures and error distribution.