  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.
