Information Decomposition on Structured Space

TL;DR

This paper develops an information geometric framework for decomposing information in structured, partially ordered variable spaces, enabling analysis of complex interactions in various scientific fields.

Contribution

It introduces a novel geometric approach to decompose information in structured spaces, extending Amari's hierarchical decomposition to new applications.

Findings

Efficient algorithms for information decomposition in structured spaces.

Application to high-order interactions in neuroscience, biology, and machine learning.

Generalization of Amari's hierarchical information decomposition.

Abstract

We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient decomposition algorithms. This generalization of Amari's seminal work on hierarchical decomposition of probability distributions on event combinations enables us to analyze high-order statistical interactions arising in neuroscience, biology, and machine learning.