LFD Book Forum Exercise 2.13
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#1
10-23-2014, 07:43 PM
 mahaitao Junior Member Join Date: Oct 2014 Posts: 6
Exercise 2.13

In Exercise 2.13 (a), Prove dvc(H)<=log_2M. How to think this problem? M is the number of hypotheses, what is the relationship between dvc and M?

(b) What does dvc(\cap H_k) and \cap H_k the intersection of hypotheses mean? How can we intersect hypotheses?
#2
10-24-2014, 10:54 PM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Exercise 2.13

For (a), maybe it is worth thinking about the dichotomies that can be generated by hypotheses?

For (b), the intersection and union of hypothesis "sets" are simply "set" intersection and union.

http://en.wikipedia.org/wiki/Union_%28set_theory%29

Hope this helps.
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When one teaches, two learn.
#3
10-26-2014, 04:50 PM
 mahaitao Junior Member Join Date: Oct 2014 Posts: 6
Re: Exercise 2.13

Professor Lin,
I think that I did not represent my question clear.

In perceptron example, we have only one H that is a set of infinite lines in the plane. My question is if we consider that H is a union of some subsets, what are they? They are subsets of these infinite lines? How to distinguish them?

And how about intersection of these subsets?
#4
10-29-2014, 01:56 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Exercise 2.13

For instance, the union of "positive rays" and "negative rays" is "positive or negative rays" which is simply 1-D perceptron. Similarly, you can have perceptrons with , and perceptrons with . Their union is all perceptrons; their intersection is perceptrons with ---that is, perceptrons that pass the origin. Hope this helps.
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When one teaches, two learn.
#5
10-30-2014, 04:28 PM
 mahaitao Junior Member Join Date: Oct 2014 Posts: 6
Re: Exercise 2.13

I got it. Thanks for your patience, professor Lin.

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