Higher order correlations in recurrent network model
Neurons are not isolated units, but highly interact. What is the best statistical description for such an interactive network of spiking neurons which still remains analytically tractable? Hawkes (1971) proposed a powerful and tractable model, now known as the Hawkes process, that describes the interaction between point emission units. In particular, Hawkes calculated the spiking correlation function in this recurrent network. In this project we calculate analytically higher order moments in this model. This is of particular relevance if we want to calculate the effect of synaptic plasticity in such a recurrent network. Indeed, in previous work, we have been showing that synaptic plasticity not only depends on the correlation between the pre- and postsynaptic activity, but can also depend on higher order correlations such as triplet correlations.