We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with variable-length memory. Each chain describes the activity of a single neuron, indicating whether it spikes at a given time. One neuron's influence on another can be either excitatory or inhibitory. To identify the existence and nature of an interaction between a neuron and its postsynaptic counterpart, we propose a model selection procedure based on the observation of the spike activity of a finite set of neurons over a finite time. The proposed procedure is also based on the maximum likelihood estimator for the synaptic weight matrix of the network neuronal model. In this sense, we prove the consistency of the maximum likelihood estimator {followed} by a proof of the consistency of the neighborhood interaction estimation procedure. The effectiveness of the proposed model selection procedure is demonstrated using simulated data, which validates the underlying theory. The method is also applied to analyze spike train data recorded from hippocampal neurons in rats during a visual attention task, where a computational model reconstructs the spiking activity and the results reveal interesting and biologically relevant information.

翻译：本文研究了从具有可变长度记忆的随机神经元的发放活动中识别其功能交互作用的问题。该神经元网络被建模为一个具有可变长度记忆的交互点过程随机系统。每条链描述单个神经元的活动，指示其在给定时刻是否发放脉冲。一个神经元对另一个神经元的影响可以是兴奋性的或抑制性的。为了识别一个神经元与其突触后对应神经元之间是否存在交互作用及其性质，我们提出了一种基于在有限时间内观察有限神经元集合的脉冲活动的模型选择方法。所提出的方法也基于对网络神经元模型的突触权重矩阵的最大似然估计。在此意义上，我们证明了最大似然估计的一致性，并随后证明了邻域交互作用估计过程的一致性。通过模拟数据验证了所提模型选择方法的有效性，从而验证了其理论基础。该方法还被应用于分析在大鼠执行视觉注意任务期间从海马神经元记录的脉冲序列数据，其中计算模型重建了发放活动，结果揭示了有趣且具有生物学意义的信息。