Multivariate linear and nonlinear causality tests

The traditional linear Granger test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones [19] develop a nonlinear Granger causality test in bivariate settings to investigate the nonlinear causality between stock prices and trading volume. This paper extends their work by developing a nonlinear causality test in multivariate settings.     

非线性格兰杰因果关系在计算神经科学的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系的应用越来越广泛,但都是用来分析线性时间序列数据之间的内在联系。将线性格兰杰因果关系推广到非线性的情形,首先利用核函数的方法建立非线性时间序列模型,再按照线性格兰杰因果关系的基本思想定义非线性格兰杰因果关系,最后通过一个模拟的例子验证该方法的有效性。模拟数据的结果表明,该方法能有效地分析非线性数据之间的内在联系。     

Granger 相关性与时间序列预测

提出一种将Granger相关信息用于时间序列预测的方法,以解决时间序列预测过程中信息利用不完全的问题.首先,通过Granger相关性检验确定时间序列系统中的可利用信息;然后,利用神经网络将可利用信息抽取出来;最后,将抽取的可利用信息融入到时间序列的预测中.实验结果验证了所提出预测方法的有效性和稳定性.     

向量自回归模型Granger因果图的条件互信息辨识与应用

Grangerl因果性是衡量系统变量间动态关系的重要依据．传统的两变量Grangerl因果分析法容易产生伪因果关系,且不能刻画变量间的即时因果性．本文利用图模型方法研究时间序列变量间的Grangerl因果关系,建立了时间序列Granger因果图,提出Grangerl因果图的条件互信息辨识方法,利用混沌理论中的关联积分估计条件互信息,统计量的显著性由置换检验确定．仿真结果证实了方法的有效性,并利用该方法研究了空气污染指标以及中国股市间的Grangerl因果关系．     

多元时间序列因果关系分析研究综述

多元时间序列的因果关系分析是数据挖掘领域的研究热点. 时间序列数据包含着与时间动态有关的、未知的、有价值的信息, 因此若能挖掘出这些知识进而对时间序列未来趋势进行预测或干预, 具有重要的现实意义. 为此, 本文综述了多元时间序列因果关系分析的研究进展、应用与展望. 首先, 本文归纳了主要的因果分析方法, 包括Granger因果关系分析、基于信息理论的因果分析和基于状态空间的因果分析; 然后, 总结了不同方法的优缺点、适用范围和发展方向, 并概述了其在不同领域的典型应用; 最后, 讨论了多元时间序列因果分析方法待解决的问题和未来研究趋势.     

Root cause diagnosis of plant-wide oscillations using Granger causality

Oscillations are common in closed-loop controlled processes which, once generated, can propagate along process flows and feedback paths of the whole plant. It is important to detect and diagnose such oscillations to maintain high control performance. This paper presents a new data-driven time series method for diagnosing the sources and propagation paths of plant-wide oscillations. The proposed method first uses a latent variable method to select features which carry significant common oscillations, then applies both time-domain Granger causality and spectral Granger causality to provide reliable diagnosis of oscillation sources and propagations. Simulation tests and an industrial case study are shown to demonstrate the effectiveness of the proposed method.     

矢量格兰杰因果关系及其在复杂网络中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在构造生物网络(基因网络、蛋白质网络、神经网络)的结构方面的应用越来越广泛,但是它只能用于研究单个节点和单个节点之间的内在联系。而实际的生物网络由于基因、神经元等的相互作用,往往呈现出非常复杂的网络结构,需要研究网络节点构成的组与组之间的内在联系。将格兰杰因果关系进行推广,得到矢量格兰杰因果关系的研究方法,并通过两个模拟的例子验证了方法的有效性。     

频域格兰杰因果关系及其在信号处理中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在信号处理、计算神经科学等许多领域的应用越来越广。人们可以利用格兰杰因果关系来分析多个变量之间的直接的相互作用,从而进一步研究各类变量之间的内在联系。以往都是在时域空间进行分析的,也就是说分析的对象都是时间序列数据,研究这些变量之间随着时间的变化是如何联系的。在时域空间的基础上,进一步从频域空间上对变量进行研究,分析在哪个频率段上变量之间存在相互作用,所得到的结论当然更具有意义。     

Causality analysis of neural connectivity: New tool and limitations of spectral Granger causality

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series based on the estimated linear regression model and has been widely applied in economics and neuroscience due to its simplicity, understandability and easy implementation. Especially, its counterpart in frequency domain, spectral GC, has recently received growing attention to study causal interactions of neurophysiological data in different frequency ranges. In this paper, on the one hand, for one equality in the linear regression model (frequency domain) we point out that all items at the right-hand side of the equality make contributions (thus have causal influence) to the unique item at the left-hand side of the equality, and thus a reasonable definition for causality from one variable to another variable (i.e., the unique item) should be able to describe what percentage the variable occupies among all these contributions. Along this line, we propose a new spectral causality definition. On the other hand, we point out that spectral GC has its inherent limitations because of the use of the transfer function of the linear regression model and as a result may not reveal real causality at all and lead to misinterpretation result. By one example we demonstrate that the results of spectral GC analysis are misleading but the results from our definition are much reasonable. So, our new tool may have wide potential applications in neuroscience.     

融合先验约束的拓扑霍克斯过程格兰杰因果发现算法

离散时序数据的格兰杰因果关系发现算法具有重要应用价值。现有方法主要采用霍克斯过程建模,无法适用于非独立同分布数据和带有时间误差的数据。为此,提出了一种融合先验约束的拓扑霍克斯过程格兰杰因果关系发现算法（PTHP）。首先,使用基于约束的方法筛选出一批显著性水平较高的因果边,提升算法对故障发生时间误差的容忍性;随后,将上一步获取的边作为先验约束融合到拓扑霍克斯过程中,解决序列间的非独立同分布问题。模拟数据和真实数据的实验证明了该方法的有效性,并获得了PCIC 2021因果推理大赛第一名。     

Simplified Granger causality map for data-driven root cause diagnosis of process disturbances

Root cause diagnosis is an important step in process monitoring, which aims to identify the sources of process disturbances. The primary challenge is that process disturbances propagate between different operating units because of the flow of material and information. Data-driven causality analysis techniques, such as Granger causality (GC) test, have been widely adopted to construct process causal maps for root cause diagnosis. However, the generated causal map is over-complicated and difficult to interpret because of the existence of process loops and the violation of statistical assumptions. In this work, a two-step procedure is proposed to solve this problem. First, a causal map is built by adopting the conditional GC analysis, which is viewed as a graph in the next step. In this graph, each vertex corresponds to a process variable under investigation, while the weight of the edge connecting two vertices is the F-value calculated by conditional GC. This graph is then simplified by computing its maximum spanning tree. Thus, the results of the causality analysis are transformed into a directed acyclic graph, which eliminates all loops, highlights the root cause variable, and facilitates the diagnosis. The feasibility of this method is illustrated with the application to the Tennessee Eastman benchmark process. In the investigated case studies, the proposed method outperforms the conditional GC test and provides an easy way to identify the root cause of process disturbances.     

Spurious Granger causality between a broken-trend stationary process and a stochastic trend process

This paper examines spurious Granger causality between a trend stationary process with structural breaks and a stochastic trend process. Monte Carlo simulations show that whether or not there are deterministic variables in the testing models, the sample size and the parameter values of the data generation process can affect the empirical frequencies of spurious Granger causality relations in different degrees. The analysis also points out that an alternative rank-based causality test method can avoid the risk of spurious causality to some extent by adopting an intercept and deterministic trend term in the testing regressions.     

Determination of ECoG information flow activity based on Granger causality and Hilbert transformation

Analysis of directional information flow patterns among different regions of the brain is important for investigating the relation between ECoG (electrocorticographic) and mental activity. The objective is to study and evaluate the information flow activity at different frequencies in the primary motor cortex. We employed Granger causality for capturing the future state of the propagation path and direction between recording electrode sites on the cerebral cortex. A grid covered the right motor cortex completely due to its size (approx. 8 cm × 8 cm) but grid area extends to the surrounding cortex areas. During the experiment, a subject was asked to imagine performing two activities: movement of the left small finger and/or movement of the tongue. The time series of the electrical brain activity was recorded during these trials using an 8 × 8 (0.016–300 Hz band with) ECoG platinum electrode grid, which was placed on the contralateral (right) motor cortex. For detection of information flow activity and communication frequencies among the electrodes, we have proposed a method based on following steps: (i) calculation of analytical time series such as amplitude and phase difference acquired from Hilbert transformation, (ii) selection of frequency having highest interdependence for the electrode pairs for the concerned time series over a sliding window in which we assumed time series were stationary, (iii) calculation of Granger causality values for each pair with selected frequency. The information flow (causal influence) activity and communication frequencies between the electrodes in grid were determined and shown successfully. It is supposed that information flow activity and communication frequencies between the electrodes in the grid are approximately the same for the same pattern. The successful employment of Granger causality and Hilbert transformation for the detection of the propagation path and direction of each component of ECoG among different sub-cortex areas were capable of determining the information flow (causal influence) activity and communication frequencies between the populations of neurons successfully.     

软件老化的多元时间序列分析方法

针对目前软件老化分析中的单参数模型,以及未考虑变量间关联性和影响性的多参数模型的不足,提出了运用多元时间序列模型分析软件老化的方法。通过对实验采集的HelixServer-VOD服务器性能数据的分析,运用格兰杰因果性检验,证实了软件老化发生和发展过程中各个性能参数间存在显著的相互影响性。引入向量自回归模型对软件老化进行建模,给出了软件老化在多个参数维度的联合预测以及参数间相互影响方式的定量描述。通过模型的迭代计算,比较了向量自回归模型与现行的未考虑参数间相互影响的模型对多个性能参数变化曲线的拟合及预测情况,证实了VAR模型更接近软件老化的本质。     

运用偏相关因果分析推断神经网络的真实结构

自从格兰杰提出因果关系的概念之后,格兰杰因果关系在构造神经网络的结构方面的应用越来越广泛,因为它可以得到神经网络的一个有向图。对于只有两个神经元的神经元网络,可以用通常的格兰杰因果关系去分析它们谁是因,谁是果。对于三个神经元以上的神经网络,由于神经元之间存在间接的作用,就不能象对两个神经元直接运用格兰杰因果关系去研究它们之间的结构了,而要用偏相关因果关系进行分析。论文介绍了偏相关因果关系的基本概念,并对一个模拟的三个神经元的网络比较了格兰杰因果关系和偏相关因果关系的区别。     

Granger因果关系检验在攻击检测中的应用研究

在时态数据挖掘框架下,对基于Granger因果关系检验的攻击检测方法进行了研究。通过计算多个前兆输入时间序列与给定异常输出时间序列之间的因果关联程度,可从描述网络系统安全状态的多元时间序列数据集中检测出网络攻击行为的前兆,进而形成可供实际检测和预警使用的高置信度前兆规则和因果规则。对所提方法的正确性和精度进行了验证,并在设计的攻击检测与预警原型系统中对其进行了应用分析。     

Predicting software defects with causality tests

In this paper, we propose a defect prediction approach centered on more robust evidences towards causality between source code metrics (as predictors) and the occurrence of defects. More specifically, we rely on the Granger causality test to evaluate whether past variations in source code metrics values can be used to forecast changes in time series of defects. Our approach triggers alarms when changes made to the source code of a target system have a high chance of producing defects. We evaluated our approach in several life stages of four Java-based systems. We reached an average precision greater than 50% in three out of the four systems we evaluated. Moreover, by comparing our approach with baselines that are not based on causality tests, it achieved a better precision.     

基于shapelets学习的多元时间序列分类

多元时间序列广泛存在于日常生活中的各个领域,多元时间序列分类是从时间序列数据中获取信息的基本方法。目前,时间序列分类研究面临着相似性度量方法特殊、原始数据维度高等问题,现有的多元时间序列分类方法的分类性能仍有待提高。文中提出一种基于shapelets学习的多元时间序列分类方法。首先,提出了新的正则化最小二乘损失学习框架下的shapelets学习方法,在此基础上采用基于shapelets的一元时间序列分类方法对多元时间序列的每维一元数据进行分类,随后由各维上的分类结果投票决定多元时间序列的最终分类结果。实验证明,所提方法在多元时间序列分类问题中能够取得较高的分类精度。     

多元混沌时间序列的因子回声状态网络预测模型

针对采用回声状态网络预测多元混沌时间序列时存在的病态解问题, 本文建立了因子回声状态网络模型, 通过因子分析(Factor analysis, FA)方法提取高维储备池状态矩阵的公因子, 去除冗余和噪声成分. 利用降维后的因子变量与期望输出之间的线性回归关系, 求解网络未知参数. 基于Lorenz序列和大连月平均气温--降雨量的仿真实验验证了本文所提模型的有效性.     

基于滑动窗口的多变量时间序列异常数据的挖掘

与其它多变量时间序列(MTS)子序列显著不同的子序列,称为异常子序列(含异常数据)。该文提出了一种基于滑动窗口的MTS异常子序列的挖掘算法,使用扩展的Frobenius 范数来计算两个MTS子序列之间相似性,使用两阶段顺序查询来进行K-近邻查找,将不可能成为候选异常子序列的MTS子序列剪去,对上海证券交易所股票交易情况MTS数据集进行了异常子序列(含异常数据)挖掘,结果表明了算法的有效性。