Foundations of Machine Learning, second edition (Adaptive Computation and Machine Learning series)

This second edition of *Foundations of Machine Learning* serves as a comprehensive graduate-level textbook and a vital reference for researchers, focusing specifically on the analysis and theory of algorithms. The book provides a general introduction to machine learning, covering fundamental modern topics while establishing the necessary theoretical basis and conceptual tools for justifying algorithms. It is distinct in its emphasis on theoretical analysis, aiming to present novel concepts with concise proofs, even for advanced subjects. The initial four chapters establish the theoretical groundwork, including the Probably Approximately Correct (PAC) learning framework and generalization bounds based on Rademacher complexity and VC-dimension, allowing subsequent chapters to function as mostly self-contained units. The text explores a wide array of critical subjects, such as Support Vector Machines (SVMs), kernel methods, boosting, on-line learning, and multi-class classification. It also delves into ranking, regression, algorithmic stability, dimensionality reduction, learning automata, and reinforcement learning. To support student learning, each chapter concludes with a set of exercises, more than half of which are new to this edition. The book also addresses practical applications, describing key aspects of how these algorithms are implemented in real-world scenarios. Comprehensive appendixes offer additional material, including a concise review of probability theory to ensure readers have the necessary mathematical background. Significant updates in this new edition include three entirely new chapters focused on model selection, maximum entropy models, and conditional entropy models. The appendixes have also been expanded to include a major section on Fenchel duality, broader coverage of concentration inequalities, and a new entry on information theory. By combining rigorous theoretical foundations with modern algorithmic discussions, this textbook equips students and researchers with the tools needed to understand and advance the field of machine learning.