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Kernel Methods for Nonlinear Connectivity Detection

1
Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Department of Atmospheric Sciences, University of São Paulo, São Paulo 05508-090, Brazil
2
Escola Politécnica, Department of Telecommunications and Control Engineering, University of São Paulo, São Paulo 05508-900, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 610; https://doi.org/10.3390/e21060610
Received: 1 May 2019 / Revised: 14 June 2019 / Accepted: 15 June 2019 / Published: 20 June 2019
(This article belongs to the Special Issue Information Dynamics in Brain and Physiological Networks)
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Abstract

In this paper, we show that the presence of nonlinear coupling between time series may be detected using kernel feature space F representations while dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. This is done by showing that the kernelized auto/cross sequences in F can be computed from the model rather than from prediction residuals in the original data space X . Furthermore, this allows for reducing the connectivity inference problem to that of fitting a consistent linear model in F that works even in the case of nonlinear interactions in the X -space which ordinary linear models may fail to capture. We further illustrate the fact that the resulting F -space parameter asymptotics provide reliable means of space model diagnostics in this space, and provide straightforward Granger connectivity inference tools even for relatively short time series records as opposed to other kernel based methods available in the literature. View Full-Text
Keywords: nonlinear time series; nonlinear-Granger causality; inference nonlinear time series; nonlinear-Granger causality; inference
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Massaroppe, L.; Baccalá, L.A. Kernel Methods for Nonlinear Connectivity Detection. Entropy 2019, 21, 610.

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