Maximum-entropy models have been successfully applied to neuronal data stemming from diverse areas like cortex, hippocampus or the retina. Despite this success, it features the major drawback of being restricted to describing every neuron to be in one out of two states: in a given time bin, either there was at least one spike or not. This property does not only limit the statistics that can be matched, but also prevents capturing the neurons’ behavior when the firing rate is high, that is when the amount of transmitted information is large.
The spike-count model we are suggesting provides a solution to both of these caveats. We are assuming the single-neuron probability distribution to be given in Boltzmann form with the energy function h*n +J*n**2 +ϵ*n**3 −ln(n!) , where n is the spike count in the respective time bin and ϵ is a small hyper parameter guaranteeing stability.
To account for pairwise covariances, we extend the independent neuron case by including an Ising-like interaction term that couples neurons in the network. To infer the model parameters, we develop Monte-Carlo and mean-field methods. We are confident that these techniques will prove useful in the further investigation of neuronal data, in particular in the search for second-order phase transitions.