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：我们解决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的问题。该神经元网络通过一个具有可变长度记忆的交互点过程随机系统建模。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。一个神经元对另一个神经元的影响可以是兴奋性或抑制性的。为了识别一个神经元与其突触后对应神经元之间交互的存在性和性质，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发放活动的模型选择程序。所提出的程序也基于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量的一致性，随后证明了邻域交互估计程序的一致性。使用模拟数据证明了所提出的模型选择程序的有效性，从而验证了基础理论。该方法还被应用于分析大鼠海马神经元在执行视觉注意任务期间记录的发放序列数据，其中一个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。