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Modeling and interpreting spike train data is a task of central importance incomputational neuroscience, with significant translational implications. Twopopular classes of data-driven models for this task are autoregressive PointProcess Generalized Linear models (PPGLM) and latent State-Space models (SSM)with point-process observations. In this letter, we derive a mathematicalconnection between these two classes of models. By introducing an auxiliaryhistory process, we represent exactly a PPGLM in terms of a latent, infinitedimensional dynamical system, which can then be mapped onto an SSM by basisfunction projections and moment closure. This representation provides a newperspective on widely used methods for modeling spike data, and also suggestsnovel algorithmic approaches to fitting such models. We illustrate our resultson a phasic bursting neuron model, showing that our proposed approach providesan accurate and efficient way to capture neural dynamics.

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