Errata
This section collects ideas for improvements of the book and errors we found. For each error, please specify the chapter and the exact location with a short description of the error or imprecision and an idea on how to improve the part.
Chapter 3
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On the page 46, the Bayes Optimal Predictor is discussed, but the proof of the claim about it is left for the exercise: “see Exercise 7”. Even though it is written, that it is “easy to verify”, for the sake of understandability it would probably be better to show the proof.
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For the definition of Agnostic PAC (page 46), explanation of the word “Agnostic” can probably can help readers to better understand the concept. For example: “Agnostic in this context means doubtful or uncertain about the existence of something”.
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The use case for the remark 3.2 (page 49) is not clear. Probably some clarification like “The “optimal” solution might be a bit outside of the hypothesis class. When it is impossible to find a solution within some constraints, it can be reasonable to relax those constraints. After relaxation, we are more likely to find a solution.”
Chapter 4
- Remark 4.1 (page 57) The “Discretization Trick” is a bit ambiguous name for the idea, which is explained there, since there is no actual trick there, but only the things, which we face in real life scenarios.
Chapter 6
Lemma 6.1 on page 68 and Theorem 6.7 case 4 on page 72 miss the realisability assumption.
Chapter 7
The epsilon function is defined on page 86 as
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Since we minimise over an open interval, the question arises whether this is always well-defined. Do we assume a “proper” agnostic case where $\epsilon =0$ never occurs?
The definition of a prefix-free description language on page 89 is a little ambiguous since a “prefix” is not precisely defined. Is a string a prefix of itself? The addition of an injectivity assumption would clarify that.
Chapter 26
Lemma 26.9 contains a typo: the last entry of $\phi(a)$ should be denoted $\phi_m(a_m)$ instead of $\phi_m(y_m)$.