InfoMat: A Tool for the Analysis and Visualization Sequential Information Transfer

TL;DR

This paper introduces InfoMat, a simple matrix visualization tool for analyzing and understanding information transfer in sequential systems, aiding in the interpretation of complex probabilistic dependencies.

Contribution

The work develops the InfoMat matrix representation, enabling visualization of information transfer and revealing new relations between sequential information measures.

Findings

InfoMat provides a new visual perspective on mutual information decomposition.

It facilitates understanding of information transfer evolution in datasets.

The tool helps visualize the impact of coding schemes on information exchange.

Abstract

Despite the popularity of information measures in analysis of probabilistic systems, proper tools for their visualization are not common. This work develops a simple matrix representation of information transfer in sequential systems, termed information matrix (InfoMat). The simplicity of the InfoMat provides a new visual perspective on existing decomposition formulas of mutual information, and enables us to prove new relations between sequential information theoretic measures. We study various estimation schemes of the InfoMat, facilitating the visualization of information transfer in sequential datasets. By drawing a connection between visual patterns in the InfoMat and various dependence structures, we observe how information transfer evolves in the dataset. We then leverage this tool to visualize the effect of capacity-achieving coding schemes on the underlying exchange of information. We believe the InfoMat is applicable to any time-series task for a better understanding of the data at hand.