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机器学习Yaser S. Abu-Mostafa, Pasadena, California. Malik Magdon-Ismail, Troy, New York. Hsuan-Tien Lin, Taipei, Taiwan. March, 2012.
The book website amlbook. com contains supporting material for instructors and readers LEARNING FROM DATA A SHORT COURSE Yaser s. abu-Mostafa California Institute of Technologg Malik Magdon-smail Rensselaer polytechnic Institute Hsuan-ien lin National Taiwan University AMlbook. com Yaser s. Abu mostaf a Malik magnon ismail Departments of Electrical Engineering Department of Computer Science and Computer Science California Institute of Technology Rensselaer Polytechnic Institute Pasadena, Ca 91125, USA Troy, NY 12180, USA yaser@caltech. edu magdon@cs. rpi. edu Hsuan Tien in Department of Computer Science and Information Engineering National Taiwan University Taipei, 106, taiwan htlingcsie. ntu. edu. tw ISBN10:1600490069 ISBN13:9781600490064 C2012 Yaser S. Abu Mostafa, Malik Magdon Ismail, Hsuan Tien Lin 1.10 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the authors. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means-electronic, mechanical, photocopying, scanning, or otherwise--without prior written permission of the authors, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act Limit of Liability/Disclaimer of Warranty: While the authors have used their best efforts in preparing this book, they make no representation or warranties with re spect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. The authors shall not be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages The use in this publication of tradenames, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights This book was typeset by the authors and was printed and bound in the United States of america To our teachers, and to our students Preface This book is designed for a short course on machine learning. It is a short course, not a hurried course. From over a decade of teaching this material, we have distilled what we believe to be the core topics that every student of the subject should know. We chose the title learning from data,that faithfully describes what the subject is about, and made it a point to cover the topics in a story-like fashion. Our hope is that the reader can learn all the fundamentals of the subject by reading the book cover to cover. Learning from data has distinct theoretical and practical tracks. If you read two books that focus on one track or the other you may feel that you are reading about two different subjects altogether. In this book, we balance the theoretical and the practical, the mathematical and the heuristic. Our criterion for inclusion is relevance. Theory that establishes the conceptual framework for learning is included, and so are heuristics that impact the per formance of real learning systems. Strengths and weaknesses of the different parts are spelled out. Our philosophy is to say it like it is: what we know what we dont know, and what we partially know The book can be taught in exactly the order it is presented. The notable exception may be Chapter 2, which is the most theoretical chapter of the book The theory of generalization that this chapter covers is central to learning from data, and we made an effort to make it accessible to a wide readership However, instructors who are more interested in the practical side may skim over it, or delay it until after the practical methods of Chapter 3 are taught You will notice that we included exercises (in gray boxes) throughout the text. The main purpose of these exercises is to engage the reader and enhance understanding of a particular topic being covered. Our reason for separating the exercises out is that they are not crucial to the logical fow. Nevertheless, they contain useful information, and we strongly encourage you to read them even if you don't do them to completion. Instructors may find some of the exercises appropriate as 'easy' homework problems, and we also provide ad ditional problems of varying difficulty in the Problems section at the end of each chapter. To help instructors with preparing their lectures based on the book, we provide supporting material on the book's website(AMLbook. com). There is also a forum that covers additional topics in learning from data. We will PREFACE discuss these further in the epilogue of this book Acknowledgment(in alphabetical order for each group): We would like to express our gratitude to the alumni of our Learning Systems group at caltech who gave us detailed expert feedback: Zehra Cataltepe, Ling Li, Amrit Pratap and Joseph sill. We thank the many students and colleagues who gave us useful feedback during the development of this book, especially Chun-Wei Liu. The Caltech Library staff, especially Kristin Buxton and David McCaslin, have given us excellent advice and help in our self-publishing effort. We also thank Lucinda acosta for her help throughout the writing of this book Last, but not least, we would like to thank our families for their encourage ment, their support, and most of all their patience as they endured the time demands that writing a book has imposed on us Yaser S. Abu-Mostafa, Pasadena, California Malik Magdon-Ismail, Troy, New york Hsuan- Tien Lin, Taipei, Taiwan Me 9012. Contents Preface 1 The Learning Problem 1.1 Problem Setup 1.1.1 Components of learning 1. 1.2 A Simple learning Model 1359 1.1.3 Learning versus Design 1. 2 Types of Learning 1.2.1 Supervised Learning 1.2.2 Reinforcement Learning 1.2.3 Unsupervised Learning 1.2.4 Other views of learning 14 1. 3 Is Learning Feasible? 15 1.3.1 Outside the data Set 16 1.3.2 Probability to the rescue 1.3.3 Feasibility of Learning 24 1.4 Error and noise 1.4.1 Error measures 28 1.4.2 Noisy Targets 1.5 Problems 2 Training versus Testing 2.1 Theory of generalization 39 2.1.1 Effective Number of hypotheses 41 2.1.2 Bounding the growth Function 46 2.1.3 The vc Dimension 50 2.1.4 The Vc generalization bound 53 2.2 Interpreting the Generalization Bound 55 2.2.1 Sample Complexity 57 2.2.2 Penalty for Model Complexity 2.2.3 The Test Set 59 2.2.4 Other Target Types 61 2.3 Approximation-Generalization Tradeoff 62

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