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 4344), 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.