Title: Identification of a stochastic resonate-and-fire neuronal model via nonlinear least squares and maximum likelihood estimation

Authors: Jun Chen; Peter Molnar; Aman Behal

Addresses: Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, Florida 32817, USA ' Department of Zoology, Savaria Campus, University of West Hungary, Karolyi Gaspar ter 4. Szombathely, H-9700, Hungary ' Department of Electrical Engineering and Computer Science and NanoScience Technology Center, University of Central Florida, Orlando, Florida 32817, USA

Abstract: Recent work has shown that the resonate-and-fire neuronal model is both computationally efficient and suitable for large network simulations. In this paper, we examine the estimation problem of a resonate-and-fire neuronal model with stochastic firing threshold. The model parameters are divided into two sets. The first set is associated with the subthreshold behaviour and can be estimated by a least squares algorithm, while the second set includes parameters associated with the firing threshold and its identification is formulated as a maximum likelihood estimation problem. The latter is in turn solved by a simulated annealing approach that avoids local optima. The proposed identification approach is evaluated using both simulated and in-vitro data, which shows a good match between prediction by identified model and the actual data, concluding the efficiency and accuracy of the proposed approach.

Keywords: resonate-and-fire; neuronal model; stochastic threshold; parameter estimation; maximum likelihood; simulated annealing.

DOI: 10.1504/IJMIC.2017.086565

International Journal of Modelling, Identification and Control, 2017 Vol.28 No.3, pp.221 - 231

Received: 23 Aug 2016
Accepted: 23 Oct 2016

Published online: 11 Aug 2017 *

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