A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials
A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials
复制标题
DOI：
10.1016/j.neuroimage.2009.12.110
复制
发表时间：
2010-04-15
期刊：
影响因子：
5.7
通讯作者：
Witte, Herbert
中科院分区：
文献类型：
--
作者：
Milde, Thomas;Leistritz, Lutz;Witte, Herbert
在这个方法研究中，我们提出了一个新版本的卡尔曼滤波技术来估计高维时变（TV）多元自回归（tvMVAR）模型。它是基于一个扩展的状态空间模型的多元时间序列的矩阵状态空间模型的多试验多元时间序列。其结果是一个通用的线性卡尔曼滤波器（GLKF）。GLKF实现了tvMVAR模型估计，该模型估计被应用于模拟数据和高维多试验激光诱发脑电位（LEP）的交互分析。本文采用tv部分格兰杰因果指数（tvpGCI）研究激光伤害性刺激诱发的LEPs之间的相互作用模式。首先，将新方法与具有遗忘因子的递归最小二乘（RLS）算法的多次试验版本（Moller等人，2001）通过使用24个不同的电极。RLS因通道号（维度）大于24而失败。其次，使用所有58个电极重复分析，并讨论基于GCI的相互作用模式的相似性和差异。可以证明，高维tvMVAR建模的应用将有助于更好地理解结构和功能之间的关系。(C)2010年爱思唯尔公司All rights reserved.
In this methodological study we present a new version of a Kalman filter technique to estimate high-dimensional time-variant (tv) multivariate autoregressive (tvMVAR) models. It is based on an extension of the state-space model for a multivariate time series to a matrix-state-space model for multi-trial multivariate time series. The result is a general linear Kalman filter (GLKF). The GLKF enables a tvMVAR model estimation which was applied for interaction analysis of simulated data and high-dimensional multi-trial laser-evoked brain potentials (LEP). The tv partial Granger causality index (tvpGCI) Was used to investigate the interaction patterns between LEPs derived from an experiment with noxious laser stimulation. First, the new approach was compared with the multi-trial version of the recursive least squares (RLS) algorithm with forgetting factor (Moller et al., 2001) by using 24 distinct electrodes. The RLS failed for a channel number (dimension) higher than 24. Secondly, the analysis was repeated by using all 58 electrodes and the similarities and differences of the GCI-based interaction patterns are discussed. It can be demonstrated that the application of high-dimensional tvMVAR modelling will contribute to a better understanding of the relationship between structure and function. (C) 2010 Elsevier Inc. All rights reserved.