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Old 01-25-2013, 02:55 PM is offline
Join Date: Jul 2012
Posts: 17
Default Re: Quick clarification on the growth function

Originally Posted by geekoftheweek View Post
I agree with with this. I don't *think* I said something different above.

I think we were just meant to infer the rest. The points are placed arbitrarily in that example but if you erected a coordinate system and systematically attempted every configuration of four points they would suffer the same issue: there is a binary configuration that is not separable.
So, if I am understanding everybody's input clearly, the following steps must be followed:
1. A budget of N points is given.
2. We set up the positions of these points in the input space arbitrarily.
3. We apply all the hypotheses from the hypothesis set to generate all possible dichotomies, noting only the unique ones. While doing this, we do not change the positions of these points.
4. If all possible dichotomies are obtained, we have proven that the hypothesis set can shatter N points.
5. If all possible dichotomies are not obtained, we reposition the N points in an educated way, and repeat the experiment. Again, once the positions are set, we don't change them till we have listed all possible unique dichotomies for those positions.
6. Doing this repeatedly can give a sense of whether there is any set of positions of the N points that can be shattered. If not, N is a break point.
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