Information Theory and Statistical Learning

2026-05-04 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Advanced, short

Summary

Abbas El Gamal's manuscript, "Information Theory and Statistical Learning," is a preprint chapter intended for the forthcoming third edition of "Cover and Thomas's Elements of Information Theory." Submitted on May 4, 2026 (v1) and revised on June 18, 2026 (v2), this work provides a concise and accessible treatment of the intersection between learning and information theory, specifically focusing on model training and fundamental performance limits. It requires only basic information theory and statistics knowledge, making it suitable for senior undergraduate or first-year graduate students, complete with end-of-chapter exercises. The chapter explores the critical role of divergence measures in diverse model training contexts, such as linear and logistic regression, autoregressive models, variational autoencoders, diffusion models, generative adversarial networks, and score-based models. It introduces the evidence lower bound (ELBO), f-divergences, and Fisher divergence, notably offering a more systematic derivation for generative diffusion models than typically found in literature.

Key takeaway

For AI students or machine learning researchers seeking a foundational understanding of information theory's role in statistical learning, this chapter offers a clear, accessible resource. You should review its systematic treatment of divergence measures, ELBO, and f-divergences, particularly the explicit derivation for generative diffusion models. This material provides essential theoretical grounding and practical insights for developing and optimizing modern AI models. It will enhance your ability to characterize performance limits and improve training methodologies.

Key insights

Information theory's divergence measures are fundamental for understanding and training diverse statistical learning models.

Principles

• Divergence measures drive model training.
• Information theory defines performance limits.
• Systematic derivations clarify complex models.

Method

The chapter systematically derives concepts like ELBO, f-divergences, and Fisher divergence, applying them to various models from linear regression to generative diffusion models, with a focus on explicit derivations for complex models.

In practice

• Apply divergence measures in VAEs.
• Utilize ELBO for model optimization.
• Derive generative diffusion models systematically.

Topics

• Information Theory
• Statistical Learning
• Divergence Measures
• Generative Models
• ELBO
• Machine Learning Theory

Best for: Research Scientist, AI Student, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.