LFD Book Forum Breaking Point
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#1
01-29-2015, 05:50 AM
 ahalasa Junior Member Join Date: Jan 2015 Posts: 4
Breaking Point

In general, can we say that the break point is the point that the hypothesis function h, changes from + to - or the opposite?
#2
02-15-2015, 07:17 PM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 610
Re: Breaking Point

The breaking point does not act on one hypothesis, it acts on a whole hypothesis set. So your description may not work. Hope this helps.
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#3
03-07-2016, 01:25 AM
 lfdid Junior Member Join Date: Mar 2016 Posts: 2
Re: Breaking Point

Definition 2.3 on p. 45 of the LFD book says that "if NO data set of size k can be shattered by H, then k is the break point for H."

My understanding is that it should read: "if there is a data set of size k such that it can NOT be shattered by H, then k is the break point for H".

Is this correct?

Many thanks!
#4
03-07-2016, 01:30 AM
 lfdid Junior Member Join Date: Mar 2016 Posts: 2
Re: Breaking Point

Quote:
 Originally Posted by lfdid Definition 2.3 on p. 45 of the LFD book says that "if NO data set of size k can be shattered by H, then k is the break point for H." My understanding is that it should read: "if there is a data set of size k such that it can NOT be shattered by H, then k is the break point for H". Is this correct? Many thanks!
Apologies, "the break point" should be "a break point"
#5
04-15-2016, 09:02 PM
 ntvy95 Member Join Date: Jan 2016 Posts: 37
Re: Breaking Point

Quote:
 Originally Posted by lfdid Definition 2.3 on p. 45 of the LFD book says that "if NO data set of size k can be shattered by H, then k is the break point for H." My understanding is that it should read: "if there is a data set of size k such that it can NOT be shattered by H, then k is the break point for H". Is this correct? Many thanks!
I don't think so. For the example of Positive rays (Page 43-44), the book also says:

Quote:
 Notice that if we picked N points where some of the points coincided (which is allowed), we will get less than N + 1 dichotomies. This does not affect the value of mH(N) since it is defined based on the maximum number of dichotomies.
In the Positive intervals example, we have derived:

We observe that not all the value of k gets , indeed:

This means that for some (not all) data set of size , the hypothesis set H is able to shatter (in other words, be able to generate dichotomies). However, for any data set of size , there is no way that the hypothesis set H is able to generate dichotomies.

For example, if , the hypothesis set H is only able to generate 7 dichotomies (while ). However, even when , if the two points coincide (both have the same value of x), there is no way for H to generate dichotomies on those points.
#6
04-16-2016, 04:36 PM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 610
Re: Breaking Point

Quote:
 Originally Posted by lfdid Definition 2.3 on p. 45 of the LFD book says that "if NO data set of size k can be shattered by H, then k is the break point for H." My understanding is that it should read: "if there is a data set of size k such that it can NOT be shattered by H, then k is the break point for H". Is this correct? Many thanks!
No, it shouldn't read so. For a break point, *no* data set of such a size can be shattered. So that is a very strong condition.
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#7
12-19-2016, 04:09 AM
 anthonyhends Junior Member Join Date: Dec 2016 Posts: 1
Re: Breaking Point

I was also looking for an answer to this question. Thanks for answering this. Much appreciated
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#8
04-06-2017, 10:11 AM
 diethealthcare Banned Join Date: Apr 2017 Posts: 13
Re: Breaking Point

Great info thanks

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