Information-Theoretic Measures in AI: A Practical Decision Guide

TL;DR

This paper offers a practical decision framework for selecting and applying seven key information-theoretic measures in AI, addressing estimator choices and potential misuse across various AI contexts.

Contribution

It introduces a structured decision flowchart and table to guide measure selection, estimator choice, and safe application in AI and agent analysis.

Findings

Provides a measure-selection flowchart for AI applications.

Includes a decision table for estimator and misuse considerations.

Demonstrates framework with three practical examples.

Abstract

Information-theoretic (IT) measures are ubiquitous in artificial intelligence: entropy drives decision-tree splits and uncertainty quantification, cross-entropy is the default classification loss, mutual information underpins representation learning and feature selection, and transfer entropy reveals directed influence in dynamical systems. A second, less consolidated family of measures, integrated information (Phi), effective information (EI), and autonomy, has emerged for characterizing agent complexity. Despite wide adoption, measure selection is often decoupled from estimator assumptions, failure modes, and safe inferential claims. This paper provides a practical decision framework for all seven measures, organized around three prescriptive questions for each: (i) what question does the measure answer and in which AI context; (ii) which estimator is appropriate for the data type and dimensionality; and (iii) what is the most dangerous misuse. The framework is operationalized in two complementary artifacts: a measure-selection flowchart and a master decision table. We cover both AI/ML and decision-making agent application domains per measure, with standardized Bridge Boxes linking IT quantities to cognitive constructs. Three worked examples illustrate the framework on concrete practitioner scenarios spanning representation learning, temporal influence analysis, and evolved agent complexity.