Differentiating information transfer and causal effect

TL;DR

This paper clarifies the distinction between information transfer and causal effect, comparing transfer entropy and information flow through cellular automata to highlight their complementary roles in understanding system dynamics.

Contribution

It explicitly contrasts transfer entropy and information flow, illustrating their differences and complementary nature in analyzing causality and information transfer in complex systems.

Findings

Transfer entropy is suitable for inferring causal effects under certain conditions.

Information flow effectively describes the causal structure of a system.

The measures are complementary in analyzing emergent computation and causality.

Abstract

The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing measures, transfer entropy and information flow, which can be used separately to quantify information transfer and causal information flow respectively. We apply these measures to cellular automata on a local scale in space and time, in order to explicitly contrast them and emphasize the differences between information transfer and causality. We also describe the manner in which the measures are complementary, including the circumstances under which the transfer entropy is the best available choice to infer a causal effect. We show that causal information flow is a primary tool to describe the causal structure of a system, while information transfer can then be used to describe the emergent computation in the system.