Autoregressive Point-Processes as Latent State-Space Models: a Moment-Closure Approach to Fluctuations and Autocorrelations

TL;DR

This paper establishes a mathematical link between autoregressive point-process models and latent state-space models, offering a new perspective and algorithms for modeling neural spike train data effectively.

Contribution

It introduces a novel moment-closure approach that connects PPGLM and SSM, enabling improved modeling and interpretation of neural spike data.

Findings

Accurately captures neural dynamics in a bursting neuron model

Provides an efficient method for fitting spike train models

Offers a new theoretical framework linking two popular modeling classes

Abstract

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive Point Process Generalized Linear models (PPGLM) and latent State-Space models (SSM) with point-process observations. In this letter, we derive a mathematical connection between these two classes of models. By introducing an auxiliary history process, we represent exactly a PPGLM in terms of a latent, infinite dimensional dynamical system, which can then be mapped onto an SSM by basis function projections and moment closure. This representation provides a new perspective on widely used methods for modeling spike data, and also suggests novel algorithmic approaches to fitting such models. We illustrate our results on a phasic bursting neuron model, showing that our proposed approach provides an accurate and efficient way to capture neural dynamics.