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

Michael Rule, Guido Sanguinetti

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Number of pages34
JournalNeural Computation
Early online date27 Aug 2018
DOIs
Publication statusE-pub ahead of print - 27 Aug 2018

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