基于HSIC-GL的多元时间序列非线性Granger因果关系分析  

Nonlinear Granger Causality Analysis for Multivariate Time Series Using HSIC-GL Model

作　　者：李柏松 任伟杰 韩敏[2] LI Baisong;REN Weijie;HAN Min(Faculty of Electronic Information and Electrical Engineering,DaLian University of Technology,DaLian 116024,China;Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学电子信息与电气工程学部,辽宁大连116024 [2]大连理工大学工业装备智能控制与优化教育部重点实验室,辽宁大连116024

出　　处：《信息与控制》2021年第3期356-365,共10页Information and Control

基　　金：国家自然科学基金资助项目(61773087);中央高校基本科研业务费专项资金资助项目(DUT20LAB114,DUT2018TB06)。

摘　　要：因果分析是数据挖掘领域重要的研究课题之一.由于传统的Granger因果模型难以准确识别多变量系统的非线性因果关系,本文提出一种基于Hilbert-Schmidt独立性准则(Hilbert-Schmidt independence criterion,HSIC)的组Lasso模型的Granger因果分析方法.首先,利用HSIC将输入样本和输出样本映射到再生核Hilbert空间,克服了传统的Granger因果模型不能应用于非线性系统的缺陷.然后,建立具有组Lasso约束的回归模型,对多变量及其组派生变量进行因果分析,并采用贝叶斯信息准则进行模型选择,避免了人为设置滞后阶数和正则化参数.最后,根据HSIC-GL模型的回归系数和显著性检验结果,实现了多变量时间序列之间的非线性因果分析.通过对非线性和混沌系统的仿真实验,验证了该方法的有效性.最后将其应用于沈阳空气质量指数(AQI)和气象时间序列的因果关系分析.Causality analysis is an important research topics in the field of data mining,but traditional Granger causality models have difficulty accurately identifying the nonlinear causality of multivariable systems.We propose a novel Granger causality analysis method based on the HSIC and group Lasso(HSIC-GL)model.Firstly,we use the Hilbert-Schmidt independence criterion(HSIC)to map the input and output samples into the Hilbert space of the reproducing kernel,which overcomes the inability to apply the traditional Granger causality model to nonlinear systems.Then,we establish a regression model with group Lasso constraints,which implements a causality analysis between multivariate and group-derived variables.The Bayesian information criterion is used for model selection,which prevents the artificial setting of the lag order and regularization parameters.Lastly,based on the regression coefficients and the results of significance tests of the HSIC-GL model,a nonlinear causality analysis is performed on the multivariable time series.The effectiveness of the proposed method is verified by the results of simulations of nonlinear and chaotic systems.We successfully applied this method to the air quality index and meteorological time series in Shenyang,China.

关 键 词：多元时间序列 GRANGER因果 Hilbert-Schmidt独立性 准则 组Lasso 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]