Kernel Methods for Nonlinear Connectivity Detection

TL;DR

This paper introduces a kernel-based approach for detecting nonlinear coupling in time series, simplifying the process by avoiding the pre-image problem and enabling existing methods to be applied directly in kernel space.

Contribution

It demonstrates that nonlinear connectivity can be identified using kernel feature spaces without solving the pre-image problem, extending traditional Granger causality methods.

Findings

Kernel methods effectively detect nonlinear coupling.

Existing Granger causality techniques can be adapted with kernel computations.

No need for pre-image problem solutions in nonlinear connectivity analysis.

Abstract

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. As a consequence, the canonical methodology for model construction, diagnostics, and Granger connectivity inference applies with no change other than computation using kernels in lieu of second-order moments.