Quantifying higher-order correlations in a neuronal pool

Recent experiments involving a relatively large population of neurons have shown a very significant amount of higher-order correlations. However, little is known of how these affect the integration and firing behavior of a population of neurons beyond the second order statistics. To investigate how higher-order inputs statistics can shape beyond pairwise spike correlations and affect information coding in the brain, we consider a neuronal pool where each neuron fires stochastically. We develop a simple mathematically tractable model that makes it feasible to account for higher-order spike correlations in a neuronal pool with highly interconnected common inputs beyond second order statistics. In our model, correlations between neurons appear from q-Gaussian inputs into threshold neurons. The approach constitutes the natural extension of the Dichotomized Gaussian model, where the inputs to the model are just Gaussian distributed and therefore have no input interactions beyond second order. We obtain an exact analytical expression for the joint distribution of firing, quantifying the degree of higher-order spike correlations, truly emphasizing the functional aspects of higher-order statistics, as we account for beyond second order inputs correlations seen by each neuron within the pool. We determine how higher-order correlations depend on the interaction structure of the input, showing that the joint distribution of firing is skewed as the parameter q increases inducing larger excursions of synchronized spikes. We show how input nonlinearities can shape higher-order correlations and enhance coding performance by neural populations.