Disentangling high order effects in the transfer entropy

TL;DR

This paper introduces a novel method for transfer entropy analysis that decomposes information flow into components, effectively capturing high-order effects and their importance in complex systems like climate networks.

Contribution

It proposes a new approach to decompose transfer entropy into unique, redundant, and synergistic parts, addressing biases from high-order dependencies.

Findings

Effective in quantifying high-order effects in climate data

Identifies processes contributing to information transfer

Demonstrates improved understanding of complex interactions

Abstract

Transfer Entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias - either in deficiency or excess - during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network processes except the driver and target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, our method searches for both the multiplets of variables that maximize information flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic atoms. Our approach enables the quantification of the relative importance of high-order effects compared to pure two-body effects in information transfer between two processes, while also highlighting the processes that contribute to building these high-order effects alongside the driver. We demonstrate the application of our approach in climatology by analyzing data from El Ni\~{n}o and the Southern Oscillation.