Understanding Machine Learning: From Theory to Algorithms
1.2 When Do We Need Machine Learning? 21 rats turns out to be more complex than what one may expect. In experiments carried out ...
22 Introduction defined program. Examples of such tasks include driving, speech recognition, and image understanding. In all of ...
1.3 Types of Learning 23 illustrative example, consider the task of learning to detect spam e-mail versus the task of anomaly de ...
24 Introduction ful for achieving the learning goal. In contrast, when a scientist learns about nature, the environment, playing ...
1.5 How to Read This Book 25 special abilities of computers to complement human intelligence, often perform- ing tasks that fall ...
26 Introduction of the book is built. This part could serve as a basis for a minicourse on the theoretical foundations of ML. Th ...
1.6 Notation 27 Chapter 30. Chapters 12, 13. Chapter 14. Chapter 8. Chapter 17. Chapter 29. Chapter 19. Chapter 20. Chapter 21. ...
28 Introduction Table 1.1Summary of notation symbol meaning R the set of real numbers Rd the set ofd-dimensional vectors overR R ...
1.6 Notation 29 x 0 such that for allx > x 0 we havef(x)≤αg(x). We writef= Ω(g) if there existx 0 ,α∈R+such that for allx > ...
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Part I Foundations ...
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2 A Gentle Start Let us begin our mathematical analysis by showing how successful learning can be achieved in a relatively simpl ...
34 A Gentle Start tasted and their color, softness, and tastiness). Such labeled examples are often calledtraining examples. We ...
2.2 Empirical Risk Minimization 35 correct labeling functionf. We omit this subscript when it is clear from the context.L(D,f)(h ...
36 A Gentle Start predict the taste of a papaya on the basis of its softness and color. Consider a sample as depicted in the fol ...
2.3 Empirical Risk Minimization with Inductive Bias 37 with the lowest possible error overS. Formally, ERMH(S)∈argmin h∈H LS(h), ...
38 A Gentle Start definition2.1 (The Realizability Assumption) There existsh? ∈ H s.t. L(D,f)(h?) = 0. Note that this assumption ...
2.3 Empirical Risk Minimization with Inductive Bias 39 commonly denoted by. We interpret the eventL(D,f)(hS)> as a failure ...
40 A Gentle Start to the event∀i,h(xi) =f(xi). Since the examples in the training set are sampled i.i.d. we get that Dm({S|x:LS( ...
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