The present paper provides a mathematical description of high-order moments of spiking activity in a recurrently-connected network of Hawkes processes. It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic rate functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure. Our approach describes the spatio-temporal filtering induced by the afferent and recurrent connectivities using operators of the input moments. This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants.
from cs updates on arXiv.org https://ift.tt/2q81xHX
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