Gaussian process models for hippocampal grid cells

These notes are structured as an iPython/Jupyter notebook tutorial written in python 3, and depend only on the numpy and scipy libraries. [download as: .ipynb , .html , .pdf ]

Gaussian Processes (GPs) generalize the idea of multivariate Gaussian distributions to distributions over functions. In neuroscience, they can be used to estimate how the firing rate of a neuron varies as a function of other variables (e.g. to track retinal waves ). Lately, we've been using Gaussian processes to describe the firing rate map of hippocampal grid cells .

We review Bayesian inference and Gaussian processes, explore applications of Gaussian Processes to analyzing grid cell data, and finally construct a GP model of the log-rate that accounts for the Poisson noise in spike count data. Along the way, we discuss fast approximations for these methods, like kernel density estimation , or approximating GP inference using convolutions.

Edit: There is a bug in the "covariance_crosshairs" function, there should be a square-root around "chi2.isf(1-p,df=2)".