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首页> 外文期刊>Journal of Computational Neuroscience >Spike-triggered covariance: geometric proof, symmetry properties, and extension beyond Gaussian stimuli
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Spike-triggered covariance: geometric proof, symmetry properties, and extension beyond Gaussian stimuli

机译：尖峰触发的协方差：几何证明，对称特性和超出高斯刺激的扩展

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摘要

The space of sensory stimuli is complex and high-dimensional. Yet, single neurons in sensory systems are typically affected by only a small subset of the vast space of all possible stimuli. A proper understanding of the input-output transformation represented by a given cell therefore requires the identification of the subset of stimuli that are relevant in shaping the neuronal response. As an extension to the commonly-used spike-triggered average, the analysis of the spike-triggered covariance matrix provides a systematic methodology to detect relevant stimuli. As originally designed, the consistency of this method is guaranteed only if stimuli are drawn from a Gaussian distribution. Here we present a geometric proof of consistency, which provides insight into the foundations of the method, in particular, into the crucial role played by the geometry of stimulus space and symmetries in the stimulus-response relation. This approach leads to a natural extension of the applicability of the spike-triggered covariance technique to arbitrary spherical or elliptic stimulus distributions. The extension only requires a subtle modification of the original prescription. Furthermore, we present a new resampling method for assessing statistical significance of identified relevant stimuli, applicable to spherical and elliptic stimulus distributions. Finally, we exemplify the modified method and compare it to other prescriptions given in the literature.
机译：感觉刺激的空间是复杂且高维的。然而，感觉系统中的单个神经元通常仅受所有可能刺激的巨大空间的一小部分影响。因此，对给定细胞所代表的输入-输出转换的正确理解需要识别与塑造神经元反应有关的刺激子集。作为对常用峰值触发平均值的扩展，峰值触发协方差矩阵的分析提供了一种检测相关刺激的系统方法。按照最初的设计，仅当从高斯分布中提取刺激时，才能保证此方法的一致性。在这里，我们提供了一致性的几何证明，这为该方法的基础提供了见识，尤其是对于刺激空间的几何形状和对称性在刺激-响应关系中所起的关键作用。这种方法导致了尖峰触发协方差技术在任意球形或椭圆形刺激分布上的自然应用。扩展名仅需对原始处方进行细微修改。此外，我们提出了一种新的重采样方法，用于评估已识别的相关刺激的统计显着性，适用于球形和椭圆形刺激分布。最后，我们举例说明了改进的方法，并将其与文献中给出的其他处方进行了比较。

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