Rosenberg J R, Halliday D M, Breeze P, Conway B A
Division of Neuroscience and Biomedical Systems, Institute of Biomedical and Life Sciences, University of Glasgow, UK.
J Neurosci Methods. 1998 Aug 31;83(1):57-72. doi: 10.1016/s0165-0270(98)00061-2.
The cross-correlation histogram has provided the primary tool for inferring the structure of common inputs to pairs of neurones. While this technique has produced useful results it not clear how it may be extended to complex networks. In this report we introduce a linear model for point process systems. The finite Fourier transform of this model leads to a regression type analysis of the relations between spike trains. An advantage of this approach is that the full range of techniques for multivariate regression analyses becomes available for spike train analysis. The two main parameters used for the identification of neural networks are the coherence and partial coherences. The coherence defines a bounded measure of association between two spike trains and plays the role of a squared correlation coefficient defined at each frequency lambda. The partial coherences, analogous to the partial correlations of multiple regression analysis, allow an assessment of how any number of putative input processes may influence the relation between any two output processes. In many cases analytic solutions may be found for coherences and partial coherences for simple neural networks, and in combination with simulations may be used to test hypotheses concerning proposed networks inferred from spike train analyses.
互相关直方图为推断神经元对共同输入的结构提供了主要工具。虽然这项技术已经产生了有用的结果，但尚不清楚如何将其扩展到复杂网络。在本报告中，我们介绍了一种点过程系统的线性模型。该模型的有限傅里叶变换导致了对脉冲序列之间关系的回归类型分析。这种方法的一个优点是，多元回归分析的全套技术可用于脉冲序列分析。用于识别神经网络的两个主要参数是相干性和偏相干性。相干性定义了两个脉冲序列之间关联的有界度量，并在每个频率λ处起到平方相关系数的作用。偏相干性类似于多元回归分析中的偏相关性，允许评估任意数量的假定输入过程如何影响任意两个输出过程之间的关系。在许多情况下，可以找到简单神经网络的相干性和偏相干性的解析解，并结合模拟用于检验关于从脉冲序列分析推断出的拟议网络的假设。
