Estimating smooth and sparse neural receptive fields with a flexible spline basis

Spatio-temporal receptive field (STRF) models are frequently used to approximate the computation implemented by a sensory neuron. Typically, such STRFs are assumed to be smooth and sparse. Current state-of-the-art approaches for estimating STRFs based empirical Bayes estimation encode such prior knowledge into a prior covariance matrix, whose hyperparameters are learned from the data, and thus provide STRF estimates with the desired properties even with little or noisy data. However, empirical Bayes methods are often not computationally efficient in high-dimensional settings, as encountered in sensory neuroscience. Here we pursued an alternative approach and encode prior knowledge for estimation of STRFs by choosing a set of basis function with the desired properties: a natural cubic spline basis. Our method is computationally efficient, and can be easily applied to Linear-Gaussian and Linear-Nonlinear-Poisson models as well as more complicated Linear-Nonlinear-Linear-Nonlinear cascade model or spike-triggered clustering methods. We compared the performance of spline-based methods to no-spline ones on simulated and experimental data, showing that spline-based methods consistently outperformed the no-spline versions. We provide a Python toolbox for all suggested methods (\url{https://github.com/berenslab/RFEst/}).