Consistent model selection for estimating functional interactions among stochastic neurons with variable-length memory

Author(s)

Ferreira, Ricardo F. ; Pacola, Matheus E. ; Schiavone, Vitor G. ; Pena, Rodrigo F. O.

• Document type: Journal article
• Source: Neurocomputing; v. 640, p. 16-pg., 2025-08-01.

Abstract

We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity, where "variable-length memory" implies that the influence of past spikes can extend over time periods whose length itself may change, reflecting adaptive or context-dependent history effects. The neuronal network is modeled by a stochastic system of interacting point processes with variable-length memory, meaning that each neuron's firing probability depends on its own and other neurons' historical spikes, with the length of this history not being fixed. 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 ensuring that, with enough data, the method accurately recovers both the values of the synaptic weights and the presence or absence of connections. The effectiveness of the proposed model selection procedure is demonstrated using simulated data, which validates the underlying theory showing that, under controlled conditions, the estimated connections match the true simulated network, thereby confirming the accuracy and robustness of the approach. 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. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Oswaldo Baffa Filho
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 18/25076-3 - High Dimensional Statistical Inference for Stochastic Processes with application in Neuroscience
• Grantee: Ricardo Felipe Ferreira
• Support Opportunities: Scholarships in Brazil - Post-Doctoral