Comparison of nonlinear Granger causality extensions for low-dimensional systems.

The identification of hidden interdependences among the parts of a complex system is a fundamental issue. Typically, the objective is, given only a sequence of scalar measurements, to infer as much as possible about the internal dynamics of the system and about the interactions between its subsystems. In general, such interactions are not only nonlinear but also asymmetric.

Detecting direction of causal interactions between dynamically coupled signals.

The problem of temporal localization and directional mapping of the dynamic interdependencies between parts of a complex system is addressed. We present a technique that weights the sampled values so as to minimize the mutual prediction error between pairs of measured signals. The reliability of the detected intermittent causal interactions is maximized by (a) smoothing the weight landscape through regularization, and (b) using a nonlinear (polynomial) variant of the conventional embedding vector.