Machine Learning: A Probabilistic Perspective

This book develops a formal theory of intelligence, defining it as an agent’s capacity to achieve goals across computable environments and grounding the concept in Kolmogorov complexity, Solomonoff induction and Hutter’s AIXI framework.It shows how these idealised constructs unify prediction, compression and reinforcement learning, yielding a universal intelligence measure while exposing the impracticality of truly optimal agents due to incomputable demands. Finally, it explores how approximate implementations could trigger an intelligence explosion and stresses the profound ethical and existential stakes posed by machines that surpass human capability.

This book offers a comprehensive introduction to algorithmic information theory: it defines plain and prefix Kolmogorov complexity, explains the incompressibility method, relates complexity to Shannon information, and develops tests of randomness culminating in Martin-Löf randomness and Chaitin’s Ω. It surveys links to computability theory, mutual information, algorithmic statistics, Hausdorff dimension, ergodic theory, and data compression, providing numerous exercises and historical notes. By unifying complexity and randomness, it supplies rigorous tools for measuring information content, proving combinatorial lower bounds, and formalizing the notion of random infinite sequences, thus shaping modern theoretical computer science.

The book provides a comprehensive yet accessible introduction to probabilistic modeling and inference, covering topics like graphical models, Bayesian methods, and approximate inference. It balances theory with practical examples, making complex probabilistic concepts understandable for newcomers and useful for practitioners. Its impact lies in shaping how students and researchers approach uncertainty in machine learning, offering a unifying probabilistic perspective that has influenced research, teaching, and real-world applications across fields such as AI, robotics, and data science.