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. The effectiveness of the proposed technique is demonstrated by studying three numerical examples of dynamically coupled chaotic maps and by comparing it with two other measures of causal dependency.