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Old 08-06-2012, 01:45 PM
Andrs Andrs is offline
Join Date: Jul 2012
Posts: 47
Default Re: Question about the union of hypothesis Q10?

Thanks bzlearn!
you are right in your first assumption! I do some paraphrasing for my own understanding.
If we assume that the hypothesis set for the 2d perceptron can handle any slope and/position, the two hypothesis set should be the same. According to the set operations, the union of two identical sets is another set equal to the components. That is, there should not be any value added to the union of two 2d perceptrons.
However, if we have two different hypothesis set, e.g. a 2d perceptron (H1) and a 3d perceptron (H2), we should get a value added for the union set (H = H1 U H2). The classification result based on H should belong to either H1 or H2. It will affect the bounds for the growth function for the union set H and its vc dim.
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