Variational log-Gaussian point-process methods for grid cells

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

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

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.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

Variational log‐ Gaussian point‐process methods for grid cells

Funder: Frank Elmore FundFunder: Medical Research Council; doi: http://dx.doi.org/10.13039/501100000265Funder: Nvidia; doi: http://dx.doi.org/10.13039/100007065Funder: School of Clinical Medicine, University of Cambridge; doi: http://dx.doi.org/10.13039/501100007552Funder: Wellcome Trust; doi: http://dx.doi.org/10.13039/100010269We 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

Simultaneous representation of multiple time horizons by entorhinal grid cells and CA1 place cells.

Grid cells and place cells represent the spatiotemporal continuum of an animal's past, present, and future locations. However, their spatiotemporal relationship is unclear. Here, we co-record grid and place cells in freely foraging rats. We show that average time shifts in grid cells tend to be prospective and are proportional to their spatial scale, providing a nearly instantaneous readout of a spectrum of progressively increasing time horizons ranging hundreds of milliseconds. Average time shifts of place cells are generally larger compared to grid cells and also increase with place field sizes. Moreover, time horizons display nonlinear modulation by the animal's trajectories in relation to the local boundaries and locomotion cues. Finally, long and short time horizons occur at different parts of the theta cycle, which may facilitate their readout. Together, these findings suggest that population activity of grid and place cells may represent local trajectories essential for goal-directed navigation and planning