Causal influence in linear response models

TL;DR

This paper introduces a new measure of causal influence in linear response models, based on information flow decomposition, and compares it with existing measures like Transfer Entropy, highlighting challenges in extending to complex systems.

Contribution

It proposes a novel measure of causal influence for linear Langevin networks and analyzes its properties and limitations compared to other information-theoretic measures.

Findings

The measure captures causal influence effectively in linear response models.

Comparison shows differences and similarities with Transfer Entropy.

Identifies challenges in extending the measure to complex, feedback-rich systems.

Abstract

The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However a widely accepted formal definition of causal influence between observables is still missing. In the framework of linear Langevin networks without feedbacks (linear response models) we developed a measure of causal influence based on a decomposition of information flows over time. We discuss its main properties and compare it with other information measures like the Transfer Entropy. Finally we outline some difficulties of the extension to a general definition of causal influence for complex systems.