Variational log‐Gaussian point‐process methods for grid cells

Abstract

We present practical solutions to applying Gaussian‐process (GP) methods to calculate spatial statistics for grid cells in large environments. GPs are a data efficient approach to inferring neural tuning as a function of time, space, and other variables. We discuss how to design appropriate kernels for grid cells, and show that a variational Bayesian approach to log‐Gaussian Poisson models can be calculated quickly. This class of models has closed‐form expressions for the evidence lower‐bound, and can be estimated rapidly for certain parameterizations of the posterior covariance. We provide an implementation that operates in a low‐rank spatial frequency subspace for further acceleration, and demonstrate these methods on experimental data.

Estimating neuronal firing density: A quantitative analysis of firing rate map algorithms

“…However, there are a number of more recent and more advanced approaches which have not yet received wide adoption. These include Bayesian [ 63 ] and Gaussian process [ 64 , 65 ] methods. These computationally complex approaches could provide improvements over traditional mapping methods and will require further investigation.…”