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Variational log-Gaussian point-process methods for grid cells.

Accepted version
Peer-reviewed

Type

Article

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Authors

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.

Description

Keywords

Gaussian process, grid cells, point process, spatial statistics, variational Bayesian inference, Bayes Theorem, Grid Cells, Normal Distribution

Journal Title

Hippocampus

Conference Name

Journal ISSN

1050-9631
1098-1063

Volume Title

Publisher

Wiley
Sponsorship
Leverhulme Trust (ECF-2020-352)
Isaac Newton Trust (20.08 (h))
European Research Council (716643)
Wellcome Trust (206682/Z/17/Z)
M.E.R. is supported by a Leverhulme and Isaac Newton Trust fellowship ECF-2020-352. P.C.V is supported by MRC, Frank Elmore Fund, and University of Cambridge School of Clinical Medicine. J.K. is a Wellcome Trust/Royal Society Sir Henry Dale Fellow (206682/Z/17/Z) and is supported by Dementia Research Institute (DRICAMKRUPIC18/19), Isaac Newton Trust/Wellcome Trust ISSF/University of Cambridge Joint Research Grant, Kavli Foundation Dream Team project (RG93383), Isaac Newton Trust [17.37(t)], and NVIDIA Corporation. T.O’L. is supported by ERC grant 716643 FLEXNEURO and HFSP grant RGY0069/2017.