Understanding Machine Learning: From Theory to Algorithms by Shai Shalev-Shwartz, Shai Ben-David

By Shai Shalev-Shwartz, Shai Ben-David

Machine studying uses machine courses to find significant patters in advanced info. it truly is one of many quickest growing to be parts of machine technological know-how, with far-reaching purposes. This ebook explains the foundations at the back of the automatic studying strategy and the issues underlying its utilization. The authors clarify the "hows" and "whys" of crucial machine-learning algorithms, in addition to their inherent strengths and weaknesses, making the sphere available to scholars and practitioners in computing device technology, data, and engineering.

"This dependent e-book covers either rigorous idea and sensible equipment of desktop studying. This makes it a slightly precise source, excellent for all those that are looking to know the way to discover constitution in data."
Bernhard Schölkopf, Max Planck Institute for clever Systems

"This is a well timed textual content at the mathematical foundations of computer studying, offering a remedy that's either deep and huge, not just rigorous but in addition with instinct and perception. It provides a variety of vintage, primary algorithmic and research innovations in addition to state of the art examine instructions. this can be a nice booklet for someone attracted to the mathematical and computational underpinnings of this significant and engaging field."

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Understanding Machine Learning: From Theory to Algorithms

Machine studying uses machine courses to find significant patters in complicated information. it's one of many quickest growing to be parts of computing device technology, with far-reaching purposes. This e-book explains the rules at the back of the automatic studying procedure and the concerns underlying its utilization. The authors clarify the "hows" and "whys" of crucial machine-learning algorithms, in addition to their inherent strengths and weaknesses, making the sphere available to scholars and practitioners in computing device technology, records, and engineering.

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The basic model relies on the realizability assumption, while the agnostic variant does not impose any restrictions on the underlying distribution over the examples. We also generalized the PAC model to arbitrary loss functions. We will sometimes refer to the most general model simply as PAC learning, omitting the “agnostic” prefix and letting the reader infer what the underlying loss function is from the context. When we would like to emphasize that we are dealing with the original PAC setting we mention that the realizability assumption holds.

D. according to D, then, with probability of at least 1 − δ, S is -representative. Similar to the definition of sample complexity for PAC learning, the function m H measures the (minimal) sample complexity of obtaining the uniform convergence property, namely, how many examples we need to ensure that with probability of at least 1 − δ the sample would be -representative. The term uniform here refers to having a fixed sample size that works for all members of H and over all possible probability distributions over the domain.

2) 33 34 Learning via Uniform Convergence Finally, if we choose m≥ log (2|H|/δ) 2 2 then Dm ({S : ∃h ∈ H, |L S (h) − L D (h)| > }) ≤ δ. 6. Let H be a finite hypothesis class, let Z be a domain, and let : H × Z → [0, 1] be a loss function. Then, H enjoys the uniform convergence property with sample complexity log (2|H|/δ) m UC . H ( , δ) ≤ 2 2 Furthermore, the class is agnostically PAC learnable using the ERM algorithm with sample complexity m H ( , δ) ≤ m UC H ( /2, δ) ≤ 2 log (2|H|/δ) 2 . 1 (The “Discretization Trick”).

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