Kernel Methods for Nonlinear Connectivity Detection
Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Department of Atmospheric Sciences, University of São Paulo, São Paulo 05508-090, Brazil
Escola Politécnica, Department of Telecommunications and Control Engineering, University of São Paulo, São Paulo 05508-900, Brazil
Author to whom correspondence should be addressed.
Received: 1 May 2019 / Revised: 14 June 2019 / Accepted: 15 June 2019 / Published: 20 June 2019
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In this paper, we show that the presence of nonlinear coupling between time series may be detected using kernel feature space
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
can be computed from the model rather than from prediction residuals in the original data space
. Furthermore, this allows for reducing the connectivity inference problem to that of fitting a consistent linear model in
that works even in the case of nonlinear interactions in the
-space which ordinary linear models may fail to capture. We further illustrate the fact that the resulting
-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.
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MDPI and ACS Style
Massaroppe, L.; Baccalá, L.A. Kernel Methods for Nonlinear Connectivity Detection. Entropy 2019, 21, 610.
Massaroppe L, Baccalá LA. Kernel Methods for Nonlinear Connectivity Detection. Entropy. 2019; 21(6):610.
Massaroppe, Lucas; Baccalá, Luiz A. 2019. "Kernel Methods for Nonlinear Connectivity Detection." Entropy 21, no. 6: 610.
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