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You are here: Home Talks & Events Bernstein Seminar 2018 Matthieu Gilson, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona | Propagation of moments in Hawkes networks

Matthieu Gilson, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona | Propagation of moments in Hawkes networks

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Bernstein Seminar

What
  • Bernstein Seminar
When Dec 06, 2018
from 05:15 PM to 06:00 PM
Where Lecture Hall, Bernstein Center Freiburg
Contact Name
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Abstract

The present study 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. This mathematical framework provides a basis for the study of learning in recurrently connected networks when high-order spiking statistics are involved (e.g., triplet STDP).

 

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