[论文解读] Isolated effective coherence (iCoh): causal information flow excluding indirect paths

Roberto D. Pascual‐Marqui, RJ Biscay+6 more|arXiv (Cornell University)|Feb 20, 2014

Electrochemical Analysis and Applications被引用 7

一句话总结

本文提出了一种名为孤立有效相干性（iCoh）的新方法，通过消除间接路径的影响，估计多元时间序列中的直接因果信息流。该方法在多元自回归模型下估计偏相干性后，将无关连接设为零，从而在不被间接路径扭曲的情况下，提供更准确的直接因果相互作用的谱表示。

ABSTRACT

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherence

研究动机与目标

• 识别并解决偏定向相干性（PDC）中的一个关键缺陷，即无关连接会扭曲因果估计的频率响应。
• 开发一种新度量方法，通过抑制多元时间序列中的间接影响，隔离直接因果相互作用。
• 确保使用脑网络等电生理数据，在系统中准确表征直接因果连接的谱特性。
• 为神经科学与系统分析提供可复现的、开源的该方法实现。

提出的方法

• 在多元自回归（MVAR）模型中估计偏相干性，以量化时间序列之间的方向性连接。
• 识别并仅将感兴趣的特定方向对的连接设为零，从而有效隔离直接路径。
• 将此隔离过程应用于相干矩阵，推导出孤立有效相干性（iCoh）度量。
• 使用具有已知因果结构的模拟模型，验证该方法抑制虚假间接影响的能力。
• 使用开源代码在Free Pascal中实现该算法，并利用测试数据确保可复现性。

实验结果

研究问题

• RQ1 在多元系统中，由于间接连接的存在，偏定向相干性是否会产生误导性的频率响应？
• RQ2 能否构建一种改进的相干度量，通过消除间接路径效应来隔离直接因果相互作用？
• RQ3 在具有已知因果结构的合成数据中，所提出的孤立有效相干性（iCoh）与PDC相比表现如何？
• RQ4 在存在间接路径的情况下，iCoh在多大程度上保持了直接因果连接的真实谱特性？

主要发现

• 偏定向相干性受到无关连接的显著干扰，导致频率响应估计不准确。
• 所提出的iCoh方法成功消除了间接路径的影响，从而更准确地表示直接因果相互作用。
• 模拟示例表明，即使间接路径可能误导PDC，iCoh仍能正确识别直接连接。
• 该方法提供了稳定且可解释的直接因果流谱分解，不受间接路径干扰的影响。