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-   -   Breaking Point (http://book.caltech.edu/bookforum/showthread.php?t=4585)

ahalasa 01-29-2015 05:50 AM

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?

htlin 02-15-2015 07:17 PM

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.

lfdid 03-07-2016 01:25 AM

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!

lfdid 03-07-2016 01:30 AM

Re: Breaking Point
 
Quote:

Originally Posted by lfdid (Post 12288)
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"

ntvy95 04-15-2016 09:02 PM

Re: Breaking Point
 
Quote:

Originally Posted by lfdid (Post 12288)
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:

m_{H}(N) = \frac{1}{2}N^{2} + \frac{1}{2}N + 1

We observe that not all the value of k gets m_{H}(k) < 2^{k}, indeed:

m_{H}(k) = \frac{1}{2}k^{2} + \frac{1}{2}k + 1 = 2^{k} \Leftrightarrow k = 2

This means that for some (not all) data set of size k \leq 2, the hypothesis set H is able to shatter (in other words, be able to generate 2^{k} dichotomies). However, for any data set of size k > 2, there is no way that the hypothesis set H is able to generate 2^{k} dichotomies.

For example, if k = 3, the hypothesis set H is only able to generate 7 dichotomies (while 2^{3} = 8). However, even when k = 2, if the two points coincide (both have the same value of x), there is no way for H to generate 2^{2} = 4 dichotomies on those points.

htlin 04-16-2016 04:36 PM

Re: Breaking Point
 
Quote:

Originally Posted by lfdid (Post 12288)
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.

anthonyhends 12-19-2016 04:09 AM

Re: Breaking Point
 
I was also looking for an answer to this question. Thanks for answering this. Much appreciated

diethealthcare 04-06-2017 10:11 AM

Re: Breaking Point
 
:) Great info thanks


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