Non-parametric generalized linear model
This work addresses a fundamental problem in statistical neuroscience for researchers modeling neural encoding, offering a more flexible and automated alternative to existing methods, though it is incremental as it builds on the Gaussian process framework.
The authors tackled the problem of modeling neural spike trains with autoregressive point process models, which require burdensome model selection and tuning of temporal basis functions, by proposing a nonparametric Gaussian process approach that jointly infers filters and hyperparameters, resulting in a computationally efficient method that automatically learns filter temporal spans and is validated on simulated and real data.
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.