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Propagation of moments in Hawkes networks


Gilson, Matthieu; Pfister, Jean-Pascal (2018). Propagation of moments in Hawkes networks. arXiv 1810.09520, Institute of Neuroinformatics.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2018
Deposited On:12 Mar 2019 11:22
Last Modified:25 Sep 2019 00:27
Publisher:Arxiv - Quantitative Biology
Series Name:arXiv
OA Status:Green
Free access at:Official URL. An embargo period may apply.
Official URL:https://arxiv.org/abs/1810.09520

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