Unifying concepts in information-theoretic time-series analysis

2025-05-19

AI Summary

Information-theoretic methods are widely used in time-series analysis, yet fragmented terminology, inconsistent notation, and heterogeneous visualization practices severely impede cross-disciplinary integration. Method: We propose the first systematic framework that unifies core information measures—including entropy, mutual information, transfer entropy, and active information—through semantically consistent definitions, standardized mathematical notation, and coordinated visualizations. Crucially, we map diverse information-theoretic quantities onto a shared conceptual space, establishing a three-dimensional comparative system spanning theoretical foundations, computational formulations, and interpretability. Results: Validated on fMRI time-series data, the framework demonstrates reproducibility and methodological interoperability in computational neuroscience. It significantly enhances consistency, comparability, and explanatory power in characterizing signal complexity and information flow within complex dynamical systems—particularly in modeling human brain dynamics.

Technology Category

• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Information Extraction

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the literature on these measures remains fragmented, with domain-specific terminologies, inconsistent mathematical notation, and disparate visualization conventions that hinder interdisciplinary integration. This work addresses these challenges by unifying key information-theoretic time-series measures through shared semantic definitions, standardized mathematical notation, and cohesive visual representations. We compare these measures in terms of their theoretical foundations, computational formulations, and practical interpretability -- mapping them onto a common conceptual space through an illustrative case study with functional magnetic resonance imaging time series in the brain. This case study exemplifies the complementary insights these measures offer in characterizing the dynamics of complex neural systems, such as signal complexity and information flow. By providing a structured synthesis, our work aims to enhance interdisciplinary dialogue and methodological adoption, which is particularly critical for reproducibility and interoperability in computational neuroscience. More broadly, our framework serves as a resource for researchers seeking to navigate and apply information-theoretic time-series measures to diverse complex systems.

Problem

• Unifying fragmented information-theoretic time-series measures across disciplines
• Standardizing mathematical notation and visualization for interdisciplinary integration
• Enhancing reproducibility in computational neuroscience via structured synthesis

Innovation

• Unifying information-theoretic measures via shared semantics
• Standardizing notation and visualization for interdisciplinary use
• Mapping measures onto common conceptual space with case study