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Gaussian processes are the leading class of distributions on randomfunctions, but they suffer from well known issues including difficulty scalingand inflexibility with respect to certain shape constraints (such asnonnegativity). Here we propose Deep Random Splines, a flexible class of randomfunctions obtained by transforming Gaussian noise through a deep neural networkwhose output are the parameters of a spline. Unlike Gaussian processes, DeepRandom Splines allow us to readily enforce shape constraints while inheritingthe richness and tractability of deep generative models. We also present anobservational model for point process data which uses Deep Random Splines tomodel the intensity function of each point process and apply it to neuralpopulation data to obtain a low-dimensional representation of spiking activity.Inference is performed via a variational autoencoder that uses a novelrecurrent encoder architecture that can handle multiple point processes asinput. We use a newly collected dataset where a primate completes a pedalingtask, and observe better dimensionality reduction with our model than withcompeting alternatives.

Deep Random Splines for Point Process Intensity Estimation of Neural Population Data