LFD Book Forum Lecture 7: Shattering for d+2 points
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#1
11-01-2015, 07:02 PM
 sandeeps Junior Member Join Date: Sep 2015 Posts: 5
Lecture 7: Shattering for d+2 points

In the argument,

After we arrive at the result that

but also state that

it is concluded that H does not shatter the given d+2 points. (I understood this).

However you then stated:
"You cannot shatter your set for any set you choose. Therefore you cannot shatter any set of d+2 points"

How did we go from not shattering a given set of d+2 points to not being to shatter any set of d+2 points?
#2
11-01-2015, 11:33 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Lecture 7: Shattering for d+2 points

Quote:
 Originally Posted by sandeeps In the argument, After we arrive at the result that but also state that it is concluded that H does not shatter the given d+2 points. (I understood this). However you then stated: "You cannot shatter your set for any set you choose. Therefore you cannot shatter any set of d+2 points" How did we go from not shattering a given set of d+2 points to not being to shatter any set of d+2 points?
There were no restrictions on the choice of the points. The argument started by taking any points then proving that you cannot shatter them by going through the linear-algebra argument.
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