Understanding Machine Learning - From Theory to Algorithms.pdf

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Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics of the field, the book covers a wide array of central topics that have not been addressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for an advanced undergraduate or beginning graduate course, the text makes the fundamentals and algorithms of machine learning accessible to students and non-expert readers in statistics, computer science, mathematics, and engineering.
Understanding Machine Learning Machine learning is one of the fastest growing areas of computer science with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a princi- pled way. The book provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Fo lowing a presentation of the basics of the field, the book covers a wide array of central topics that have not been addressed by previous te books. These include a discussion of the computational complexity learning and the concepts of convexity and stability; important algorith mic paradigms including stochastic gradient descent, neural networks and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for an advanced undergraduate or beginning graduate course, the text makes the fundamentals and algorithms of machine learning accessible to stu dents and nonexpert readers in statistics, computer science, mathematics and engineering. Shai shalev-Shwartz is an Associate Professor at the School of Computer Science and Engineering at The Hebrew University, Israel Shai ben-David is a professor in the school of computer Science at the University of Waterloo, Canada UNDERSTANDING MACHINE LEARNING From Theory to Algorithms Shai Shalev-Shwartz The hebrew University, Jerusalem Shai Ben-David University of Waterloo, Canada 努 CAMBRIDGE 吸罗 UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS 32 Avenue of the americas New york. Ny10013-2473 USA Cambridge University Press is part of the University of Cambridge It furthers the Universitys mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence www.cambridge.org Informationonthistitlewww.cambridge.org/9781107057135 C Shai Shalev-Shwartz and Shai Ben-David 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements no reproduction of any part may take place without the written permission of cambridge university press First published 2014 Printed in the United States of America A catalog record for this publication is available from the British library Library of Congress Cataloging in Publication Data Isbn 978-1-107-05713-5 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLS for external or third-party Internet Web sites referred to in this publication, and does not guarantee that any content on such Web sites is, or will remain accurate or appropriate Triple-s dedicates the book to triple-M Contents Preface page Xv 1 Introduction 1.1 What Is learning? 1.2 When Do We Need Machine Learning? 3 Types of Learning 1.4 Relations to other fields 1.5 How to read This book 1.6 Notation 11346781 Part 1 Foundations 2 A Gentle start 13 2.1 A Formal Model- The Statistical Learning framework 13 2.2 Empirical Risk Minimization 5 2.3 Empirical Risk Minimization with Inductive Bias 16 2. 4 Exercises 20 3 A Formal Learning Model 22 3.1 PAC Learning 22 3.2 A More General Learning Model 23 3.3 Summary 28 3.4 Bibliographic Remarks 28 3. 5 Exercises 28 4 Learning via Uniform Convergence 31 4.1 Uniform Convergence Is Sufficient for Learnability 31 4.2 Finite Classes Are Agnostic PAC Learnable 32 4.3 Summary 34 4.4 Bibliographic Remarks 35 4.5 Exercises 35 iii Contents 5 The Bias-Complexity Tradeoff 36 5.1 The No-Free-Lunch Theorem 37 5.2 Error Decomposition 40 5.3 Summary 41 5.4 Bibliographic Remarks 41 5.5 Exercises 6 The vc-Dimension 43 6.1 Infinite-Size Classes Can Be Learnable 43 6.2 The VC-Dimension 44 6. 3 Examples 46 6.4 The Fundamental Theorem of PAC learning 48 6.5 Proof of theorem 6.7 49 6.6 Summary 6.7 Bibliographic remarks 6. 8 Exercises 54 7 Nonuniform Learnability 7.1 Nonuniform Learnability 7. 2 Structural risk minimization 7.3 Minimum Description Length and Occam's Razor 7. 4 Other Notions of Learnability-Consistency 66 7.5 Discussing the Different Notions of Learnability 67 7.6 Summary 70 7.7 Bibliographic Remarks 70 7. 8 Exercises 8 The Runtime of learning 8.1 Computational Complexity of Learning 74 8.2 Implementing the ERM Rule 76 8.4 Hardness of Learnings ut Not by a Proper erm 8.3 Efficiently Learnable, b 80 81 8.5 Summary 82 8.6 Bibliograph hic remarks 82 8.7 Exercises 83 Part 2 From Theory to Algorithms 9 Linear Predictors 89 9.1 Halfspaces 9.2 Linear Regression 9.3 Logistic Regression 97 9. 4 Summary 99 9.5 Bibliographic Remarks 9.6 Exercises 99

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