SpikeCaKe: Semi-analytic nonparametric Bayesian inference for spike-spike neuronal connectivity

Abstract

In this paper we introduce a semi-analytic variational framework for approximating the posterior of a Gaussian processes coupled through non-linear emission models. While the semi-analytic method can be applied to a large class of models, the present paper is devoted to the analysis of causal connectivity between biological spiking neurons. Estimating causal connectivity between spiking neurons from measured spike sequences is one of the main challenges of systems neuroscience. This semi-analytic method exploits the tractability of GP regression when the membrane potential is observed. The resulting posterior is then marginalized analytically in order to obtain the posterior of the response functions given the spike sequences alone. We validate our methods on both simulated data and real neuronal recordings.