  A fundamental problem in statistical neuroscience is to model how neurons
encode information by analyzing electrophysiological recordings. A popular and
widely-used approach is to fit the spike trains with an autoregressive point
process model. These models are characterized by a set of convolutional
temporal filters, whose subsequent analysis can help reveal how neurons encode
stimuli, interact with each other, and process information. In practice a
sufficiently rich but small ensemble of temporal basis functions needs to be
chosen to parameterize the filters. However, obtaining a satisfactory fit often
requires burdensome model selection and fine tuning the form of the basis
functions and their temporal span. In this paper we propose a nonparametric
approach for jointly inferring the filters and hyperparameters using the
Gaussian process framework. Our method is computationally efficient taking
advantage of the sparse variational approximation while being flexible and rich
enough to characterize arbitrary filters in continuous time lag. Moreover, our
method automatically learns the temporal span of the filter. For the particular
application in neuroscience, we designed priors for stimulus and history
filters useful for the spike trains. We compare and validate our method on
simulated and real neural spike train data.
