非线性格兰杰因果关系在睡眠生理信号分析中的应用

基于非线性格兰杰因果关系分析睡眠生理信号。分别使用多项式核函数、高斯核函数和Sigmoid核函数将低维空间数据映射到高维特征空间,在高维特征空间使用非线性格兰杰因果方法来分析睡眠生理信号。研究结果表明,脑电信号对心电信号的影响比心电信号对脑电信号的影响更为显著,脑电信号对血压信号的影响比血压信号对脑电信号的影响更为显著,血压对心电信号的影响比心电信号对血压信号的影响更为显著,而且睡眠期样本信号间的格兰杰因果关系更为显著。仿真结果验证了睡眠期信号更能客观地反映生理信号的因果关系。     

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。     

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。     

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。     

面向故障间格兰杰因果发现的霍克斯过程研究

现有因果关系建模方法应用于故障事件序列时,难以有效引入因果先验,使得算法结果过于稠密,同时在稀疏、时间精度低的数据上因果关系可靠性较差。将不同故障类型事件的因果关系建模为基于霍克斯过程的格兰杰因果关系,提出一种面向故障序列的格兰杰因果发现的霍克斯过程模型。将霍克斯过程拓展到离散时间域,解决低时间精度数据的建模问题,并通过构造基于贝叶斯信息准则的目标函数,保证因果结构稀疏性,进而利用基于EM算法与爬山法的迭代优化算法引入因果先验,提高模型的可靠性。实验结果表明,该方法在由不同参数生成的模拟数据上均表现突出,且在两个通信网络的真实数据集中,F1评分相比ADM4、MLE-SGL、TSSO和PCMCI算法提升15.18%以上。而通过引入根因标注和因果依赖性先验,算法的F1评分进一步提升22.43%以上,验证了引入先验的有效性。     

经济时间序列的非线性建模和计算机仿真计算

研究了经济类数据的非线性特征,提出利用Logistic类混沌时间序列通过一个线性滤波器来实现对该种时间序列的建模。指出经济类时间序列的功率谱具有1／f特性,其分形维数较高,而经过一个特殊的线性滤波器后,可以用一个低维的非线性系统建模。     

基于Chebyshey神经网络的非线性预测应用研究

将Chebyshev神经网络作为非线性时间序列的辨识模型,通过对过去序列样本的学习,调整网络的权值,然后预测和推断未来的序列,仿真结果表明,Chebyshev神经网络具有优良的泛化能力和预测功能。     

在QSAR中应用SVR的非线性组合预测

为提高定量构效关系(quantitative structure-activity relationship,QSAR)模型预测的精度,以支持向量回归(support vector regression,SVR)全局与局部核函数,发展出1种非线性组合方法GK-LK-SVR,其基本思路为:依均方误差(MSE)最小原则,分别基于SVR的全局与局部核函数筛选描述符后预测,实测值与不同核函数的预测值组合成混合样本,然后再依MSE最小原则基于SVR对混合样本实施核函数寻优及子模型筛选,最后以留一法完成预测。对2种化合物QSAR建模结果表明:GK-LK-SVR方法预测精度高,有望在QSAR研究中得到广泛应用。     

非线性时间序列分析的关键技术及其应用研究

非线性时间序列分析是近几年发展起来的一个崭新的研究领域,在物理、生物、地理、医学、经济等领域具有广泛的应用前景。文章介绍了时间序列分析的线性和非线性分析方法各自的特点,由于非线性时间序列分析是个比较新的领域,该文对非线性处理技术进行了初步探讨,阐述了其研究意义,分析了其关键技术、应用前景等。最后讨论了在这一新的研究领域中值得注意的几个问题。     

Multivariate out-of-sample tests for Granger causality

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. Multivariate out-of-sample tests for Granger causality are proposed and their performance is measured by a simulation study. The results are graphically represented by size-power plots. It emerges that the multivariate regression test is the most powerful among the considered possibilities. As a real data application, it is investigated whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.     

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．     

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.     

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.     

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.     

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.     

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.