Estimating the interaction graph of stochastic neural dynamics

TL;DR

This paper develops a statistical method to accurately estimate the interaction graph of stochastic neural models from spike activity data, providing guarantees without assuming stationarity or invariant measure uniqueness.

Contribution

It introduces a new estimator for the neural interaction graph with proven exponential bounds and strong consistency, applicable to non-stationary models.

Findings

Explicit exponential bounds for estimation errors

Strong consistency of the graph estimator

Applicable without stationarity assumptions

Abstract

In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the activity of a single neuron, indicating whether it spikes or not at a given time. The spiking probability of a given neuron depends on the time evolution of its presynaptic neurons since its last spike time. When a neuron spikes, its potential is reset to a resting level and postsynaptic current pulses are generated, modifying the membrane potential of all its postsynaptic neurons. The relationship between a neuron and its pre- and postsynaptic neurons defines an oriented graph, the interaction graph of the model. The goal of this paper is to estimate this graph based on the observation of the spike activity of a finite set of neurons over a finite time. We provide explicit exponential upper bounds for the probabilities of under- and overestimating the interaction graph restricted to the observed set and obtain the strong consistency of the estimator. Our result does not require stationarity nor uniqueness of the invariant measure of the process.