Temporally Smoothed Wavelet Coherence for Multivariate Point-Processes and Neuron-Firing

Gibberd, Alex and Cohen, Edward (2018) Temporally Smoothed Wavelet Coherence for Multivariate Point-Processes and Neuron-Firing. In: 2018 52nd Asilomar Conference on Signals, Systems, and Computers. IEEE, pp. 1220-1224. ISBN 9781538692189

[img]
Preview
PDF (asilomar_submitted)
asilomar_submitted.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (3MB)

Abstract

In neuroscience, it is of key importance to assess how neurons interact with each other as evidenced via their firing patterns and rates. We here introduce a method of smoothing the wavelet periodogram (scalogram) in order to reduce variance in spectral estimates and allow analysis of time-varying dependency between neurons at different scale levels. Previously such smoothing methods have only received analysis in the setting of regular real-valued (Gaussian) time-series. However, in the context of neuron-firing, observations may be modelled as a point-process which when binned, or aggregated, gives rise to an integer-valued time-series. In this paper we propose an analytical asymptotic distribution for the smoothed wavelet spectra, and then contrast this, via synthetic experiments, with the finite sample behaviour of the spectral estimator. We generally find good alignment with the asymptotic distribution, however, this may break down if the level of smoothing, or the scale under analysis is very small. To conclude, we demonstrate how the spectral estimator can be used to characterize real neuron-firing dependency, and how such relationships vary over time and scale.

Item Type:
Contribution in Book/Report/Proceedings
Additional Information:
©2018 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
ID Code:
131960
Deposited By:
Deposited On:
14 Mar 2019 10:05
Refereed?:
Yes
Published?:
Published
Last Modified:
03 Jun 2020 00:02