understanding machine learning theory-algorithms

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1 Introduction 19 1.1 What Is Learning? 19 1.2 When Do We Need Machine Learning? 21 1.3 Types of Learning 22 1.4 Relations to Other Fields 24 1.5 How to Read This Book 25 1.5.1 Possible Course Plans Based on This Book 26 1.6 Notation 27 Part I Foundations 31 2 A Gentle Start 33 2.1 A Formal Model { The Statistical Learning Framework 33 2.2 Empirical Risk Minimization 35 2.2.1 Something May Go Wrong { Overtting 35 2.3 Empirical Risk Minimization with Inductive Bias 36 2.3.1 Finite Hypothesis Classes 37 2.4 Exercises 41 3 A Formal Learning Model 43 3.1 PAC Learning 43 3.2 A More General Learning Model 44 3.2.1 Releasing the Realizability Assumption { Agnostic PAC Learning 45 3.2.2 The Scope of Learning Problems Modeled 47 3.3 Summary 49 3.4 Bibliographic Remarks 50 3.5 Exercises 50 4 Learning via Uniform Convergence 54 4.1 Uniform Convergence Is Sucient for Learnability 54 4.2 Finite Classes Are Agnostic PAC Learnable 55 Understanding Machine Learning, c 2014 by Shai Shalev-Shwartz and Shai Ben-David Published 2014 by Cambridge University Press. Personal use only. Not for distribution. Do not post. Please link to http://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning x Contents 4.3 Summary 58 4.4 Bibliographic Remarks 58 4.5 Exercises 58 5 The Bias-Complexity Tradeo 60 5.1 The No-Free-Lunch Theorem 61 5.1.1 No-Free-Lunch and Prior Knowledge 63 5.2 Error Decomposition 64 5.3 Summary 65 5.4 Bibliographic Remarks 66 5.5 Exercises 66 6 The VC-Dimension 67 6.1 Innite-Size Classes Can Be Learnable 67 6.2 The VC-Dimension 68 6.3 Examples 70 6.3.1 Threshold Functions 70 6.3.2 Intervals 71 6.3.3 Axis Aligned Rectangles 71 6.3.4 Finite Classes 72 6.3.5 VC-Dimension and the Number of Parameters 72 6.4 The Fundamental Theorem of PAC learning 72 6.5 Proof of Theorem 6.7 73 6.5.1 Sauer's Lemma and the Growth Function 73 6.5.2 Uniform Convergence for Classes of Small Eective Size 75 6.6 Summary 78 6.7 Bibliographic remarks 78 6.8 Exercises 78 7 Nonuniform Learnability 83 7.1

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