Information Theory, Inference, and Learning Algorithms (www.inference.org.uk)

"Information Theory, Inference, and Learning Algorithms" is a celebrated textbook that ties together Shannon’s information-theoretic foundations with modern probabilistic inference and practical learning algorithms. Praised as an "instant classic" by Bob McEliece, the book is notable for making deep theory accessible and actionable: it surveys core results from information theory (entropy, mutual information, Shannon’s coding theorems), error‑correcting codes (including low‑density parity‑check codes), and then builds a unified view of Bayesian inference, model selection and learning. Technically, the book emphasizes probabilistic modeling and algorithmic techniques that matter for ML practitioners and theorists: graphical models and message‑passing (belief propagation), variational approximations, Monte Carlo methods, maximum a posteriori and maximum likelihood estimation, and minimum description length principles. It draws explicit connections between compression, coding complexity and generalization, and shows how concepts like mutual information and coding limits inform algorithm design and performance bounds. For the AI/ML community this means better principled tools for designing scalable inference algorithms, understanding trade‑offs between model complexity and data, and leveraging coding theory ideas (e.g., LDPC) in robust distributed or noisy computation settings. The book’s mix of intuition, worked examples and exercises makes it a lasting reference for research and applied work.