Information-Theoretic Measures in AI: A Practical Decision Guide
For AI practitioners and researchers, this paper offers a structured guide to selecting and applying information-theoretic measures correctly, addressing a gap in existing literature that often decouples measure selection from estimator assumptions and failure modes.
This paper provides a practical decision framework for seven information-theoretic measures, including entropy, cross-entropy, mutual information, transfer entropy, integrated information, effective information, and autonomy, addressing measure selection, estimator choice, and common misuses. The framework is operationalized via a flowchart and decision table, with three worked examples.
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.