A unified framework for information integration based on information geometry

TL;DR

This paper introduces a unified information geometric framework to quantify and interpret interactions in stochastic systems, extending transfer entropy to measure integrated information related to consciousness.

Contribution

It presents a novel geometric approach to quantify interactions and introduces a new measure of integrated information for causal analysis.

Findings

Provides geometric interpretations of mutual information and transfer entropy.

Proposes a new measure of integrated information for causal interactions.

Offers insights into the relationship between system parts and consciousness.

Abstract

We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence between the actual probability distribution of the system and a constrained probability distribution where the interactions of interest are disconnected. This framework provides novel geometric interpretations of various information theoretic measures of interactions, such as mutual information, transfer entropy, and stochastic interaction in terms of how interactions are disconnected. The framework therefore provides an intuitive understanding of the relationships between the various quantities. By extending the concept of transfer entropy, we propose a novel measure of integrated information which measures causal interactions between parts of a system. Integrated information quantifies the extent to which the whole is more than the sum of the parts and can be potentially used as a biological measure of the levels of consciousness.