Semi-Analytic Nonparametric Bayesian Inference for Spike-Spike Neuronal Connectivity

Estimating causal connectivity between spiking neurons from measured spike sequences is one of the main challenges of systems neuroscience. In this paper we introduce two nonparametric Bayesian methods for spike-membrane and spikespike causal connectivity based on Gaussian process regression. For spike-spike connectivity, we derive a new semi-analytic variational approximation of the response functions of a non-linear dynamical model of interconnected neurons. 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.