#1




Exercises and Problems
Please comment on the chapter problems in terms of difficulty, clarity, and time demands. This information will help us and other instructors in choosing problems to assign in our classes.
Also, please comment on the exercises in terms of how useful they are in understanding the material.
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#2




ERRATA: Small mistake in description of Exercise 2.1
I won't "mathify" this correction, as I don't know how in this forum (my LaTex has escaped me after years of neglect!). It's a minor point, but I feel like it should be corrected. In the wording for Exercise 2.1 on page 45:
ERROR: "Verify that m_H(n) < 2^k" CORRECTION: "Verify that m_H(k) < 2^k" Thanks! 
#3




Re: ERRATA: Small mistake in description of Exercise 2.1
Quote:
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#4




Problem 2.9 : Growth function of perceptron, seems incorrect
The problem says that in case of perceptron in ddimensional space, growth function is equal to B(N,k). Consider the following case :
d = 2, implies dvc = 2+1 = 3 N = 4 B(N,k) = 15 but the maximum no. of dichotomies possible in this case is only 14 Can someone please comment if i am missing something. Thanks. Vishwajeet. 
#5




Re: Problem 2.9 : Growth function of perceptron, seems incorrect
Thanks for catching this erratum. The problem shows the upper bound based on the VC dimension. The actual growth function is given by:
. Our appologies. Quote:
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#6




Re: Problem 2.9 : Growth function of perceptron, seems incorrect
Thank you

#7




Re: Problem 2.9 : Growth function of perceptron, seems incorrect
Sorry for the delayed response here, but i still find that
is not the case for a perceptron in ddimensional space. When N=6 and d=2, this equation says , while i was able to get 38 dichotomies (by picking 6 equidistant points on the circumference of a circle). If i am missing something, then can you please point me to the proof. Thank you. 
#8




Problem 2.10
To prove :
As this is a generic statement, it has to apply to every growth function. But all we know about the growth functions (in general) is their bound, in terms of and . Also, we know that if then is an increasing function whose value is . But, if , then we can only say that is nondecreasing and is bounded by . I guess my question is that how can we prove the generic statement above. Kindly shed some light on the proof strategy. Thank you, Vishwajeet. 
#9




Possible correction to Problem 2.14 (b)

#10




Re: Possible correction to Problem 2.14 (b)
The problem, though an overestimate seems correct.
Hint: If you have points, then can implement at most dichotomies on those points. Now try to upper bound the number of dichotomies that all hypothesis sets can implement on these points and proceed from there.
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errata, growth function, perceptron 
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