A generative spike train model with time-structured higher order correlations

TL;DR

This paper introduces a new generative model for correlated neural spike trains that captures complex temporal correlations and is analytically tractable, aiding the study of neural ensemble dynamics.

Contribution

The paper presents the GTaS model, extending prior work to generate correlated spike trains with diverse temporal structures, and derives analytical expressions for cumulant densities.

Findings

The GTaS model can produce diverse correlation patterns observed in neural data.

It is analytically tractable, allowing for explicit calculation of cumulant densities.

The model helps analyze neural network responses to structured inputs.

Abstract

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.