Breaking Point

[ahalasa]

In general, can we say that the break point is the point that the hypothesis function h, changes from + to - or the opposite?

[htlin]

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]

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]

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"

[ntvy95]

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:

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.

[htlin]

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.

[anthonyhends]

I was also looking for an answer to this question. Thanks for answering this. Much appreciated

[diethealthcare]

Great info thanks