基于相关失真的线性-非线性-Poisson模型辨识
Correlation-distortion based identification of Linear-Nonlinear-Poisson models
摘要：
线性-非线性-泊松（Linear-Nonlinear-Poisson，LNP）模型是描述单个感觉神经元和运动神经元编码（刺激-反应）转换的一种流行而强大的工具。最近，人们对神经脉冲序列的二阶和更高阶相关结构以及它如何与特定编码关系相关的兴趣越来越大。当信号相关性通过特定LNP模型变换时，信号相关性的失真是可预测的，并且在某些情况下是分析上可处理的和可逆的。在这里，我们建议，LNP编码模型可以严格地从它们引起的相关变换中识别，并开发了一种用于识别白色和有色随机高斯激励下的最小相位单神经元时间内核的计算方法。与反向相关或最大似然不同，基于相关失真的识别不需要同时观察刺激-响应对-仅需要它们各自的二阶统计量。虽然在原则上过滤器内核不一定是最小相位，只有他们的频谱幅度可以唯一地确定从输出相关性，我们表明，在实践中，这种方法提供了很好的估计内核从一系列的参数模型的神经系统。最后，我们讨论了这种方法如何可能使神经模型从更广泛的实验条件和系统，及其局限性进行估计。
英文摘要：
Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and higher-order correlation structure of neural spike trains, and how it may be related to specific encoding relationships. The distortion of signal correlations as they are transformed through particular LNP models is predictable and in some cases analytically tractable and invertible. Here, we propose that LNP encoding models can potentially be identified strictly from the correlation transformations they induce, and develop a computational method for identifying minimum-phase single-neuron temporal kernels under white and colored- random Gaussian excitation. Unlike reverse-correlation or maximum-likelihood, correlation-distortion based identification does not require the simultaneous observation of stimulus-response pairs - only their respective second order statistics. Although in principle filter kernels are not necessarily minimum-phase, and only their spectral amplitude can be uniquely determined from output correlations, we show that in practice this method provides excellent estimates of kernels from a range of parametric models of neural systems. We conclude by discussing how this approach could potentially enable neural models to be estimated from a much wider variety of experimental conditions and systems, and its limitations.
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