Probably Approximately Correct

We have effective theories for very few things. Gravity is one, electromagnetism another. But for most things—whether as mundane as finding a mate or as major as managing an economy—our theories are lousy or nonexistent. Fortunately, we don't need them, any more than a fish needs a theory of water to swim; we're able to muddle through. But how do we do it? In Probably Approximately Correct, computer scientist Leslie Valiant presents a theory of the theoryless. The key is “probably approximately correct” learning, Valiant's model of how anything can act without needing to understand what is going on. The study of probably approximately correct algorithms reveals the shared computational nature of evolution and cognition, indicates how computers might possess authentic intelligence, and shows why hacking a problem can be far more effective than developing a theory to explain it. After all, finding a mate is a lot more satisfying than finding a theory of mating. Offering an elegant, powerful model that encompasses all of life's complexity, Probably Approximately Correct will revolutionize the way we look at the universe's greatest mysteries.

Presenting a theory of the theoryless, a computer scientist provides a model of how effective behavior can be learned even in a world as complex as our own, shedding new light on human nature.

From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns. How does life prosper in a complex and erratic world? While we know that nature follows patterns -- such as the law of gravity -- our everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it? In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is "probably approximately correct" algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant's theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence. Offering a powerful and elegant model that encompasses life's complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

Abstract: "This paper surveys some recent theoretical results on the efficiency of machine learning algorithms. The main tool described is the notion of Probably Approximately Correct (PAC) learning, introduced by Valiant. We define this learning model and then look at some of the results obtained in it. We then consider some criticisms of the PAC model and the extensions proposed to address these criticisms. Finally, we look briefly at other models recently proposed in computational learning theory."

Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs. The topics covered include the motivation, definitions, and fundamental results, both positive and negative, for the widely studied L. G. Valiant model of Probably Approximately Correct Learning; Occam's Razor, which formalizes a relationship between learning and data compression; the Vapnik-Chervonenkis dimension; the equivalence of weak and strong learning; efficient learning in the presence of noise by the method of statistical queries; relationships between learning and cryptography, and the resulting computational limitations on efficient learning; reducibility between learning problems; and algorithms for learning finite automata from active experimentation.

This book of the bestselling and widely acclaimed Python Machine Learning series is a comprehensive guide to machine and deep learning using PyTorch's simple to code framework. Purchase of the print or Kindle book includes a free eBook in PDF format. Key FeaturesLearn applied machine learning with a solid foundation in theoryClear, intuitive explanations take you deep into the theory and practice of Python machine learningFully updated and expanded to cover PyTorch, transformers, XGBoost, graph neural networks, and best practicesBook Description Machine Learning with PyTorch and Scikit-Learn is a comprehensive guide to machine learning and deep learning with PyTorch. It acts as both a step-by-step tutorial and a reference you'll keep coming back to as you build your machine learning systems. Packed with clear explanations, visualizations, and examples, the book covers all the essential machine learning techniques in depth. While some books teach you only to follow instructions, with this machine learning book, we teach the principles allowing you to build models and applications for yourself. Why PyTorch? PyTorch is the Pythonic way to learn machine learning, making it easier to learn and simpler to code with. This book explains the essential parts of PyTorch and how to create models using popular libraries, such as PyTorch Lightning and PyTorch Geometric. You will also learn about generative adversarial networks (GANs) for generating new data and training intelligent agents with reinforcement learning. Finally, this new edition is expanded to cover the latest trends in deep learning, including graph neural networks and large-scale transformers used for natural language processing (NLP). This PyTorch book is your companion to machine learning with Python, whether you're a Python developer new to machine learning or want to deepen your knowledge of the latest developments. What you will learnExplore frameworks, models, and techniques for machines to 'learn' from dataUse scikit-learn for machine learning and PyTorch for deep learningTrain machine learning classifiers on images, text, and moreBuild and train neural networks, transformers, and boosting algorithmsDiscover best practices for evaluating and tuning modelsPredict continuous target outcomes using regression analysisDig deeper into textual and social media data using sentiment analysisWho this book is for If you have a good grasp of Python basics and want to start learning about machine learning and deep learning, then this is the book for you. This is an essential resource written for developers and data scientists who want to create practical machine learning and deep learning applications using scikit-learn and PyTorch. Before you get started with this book, you'll need a good understanding of calculus, as well as linear algebra.

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

A new edition of a graduate-level machine learning textbook that focuses on the analysis and theory of algorithms. This book is a general introduction to machine learning that can serve as a textbook for graduate students and a reference for researchers. It covers fundamental modern topics in machine learning while providing the theoretical basis and conceptual tools needed for the discussion and justification of algorithms. It also describes several key aspects of the application of these algorithms. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning is unique in its focus on the analysis and theory of algorithms. The first four chapters lay the theoretical foundation for what follows; subsequent chapters are mostly self-contained. Topics covered include the Probably Approximately Correct (PAC) learning framework; generalization bounds based on Rademacher complexity and VC-dimension; Support Vector Machines (SVMs); kernel methods; boosting; on-line learning; multi-class classification; ranking; regression; algorithmic stability; dimensionality reduction; learning automata and languages; and reinforcement learning. Each chapter ends with a set of exercises. Appendixes provide additional material including concise probability review. This second edition offers three new chapters, on model selection, maximum entropy models, and conditional entropy models. New material in the appendixes includes a major section on Fenchel duality, expanded coverage of concentration inequalities, and an entirely new entry on information theory. More than half of the exercises are new to this edition.