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Old 04-30-2013, 04:20 AM
Elroch Elroch is offline
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Default Re: Q10 higher bound

Quote:
Originally Posted by jforbes View Post
MindExodus - very nice; I'm thoroughly convinced.





nkatz, your example has me slightly puzzled. The only way H1 can fail to shatter 2 points is if there are exactly two points:
H1 contains +- and -+, but not -- or ++
Whereas if you give it three points, it contains
+--,
-+-,
--+,
++-,
+-+, and
-++.
Just looking at the first two points, now H1 contains all 4 combinations. How can this be if its VC dimension is only 1? I think it must be the case that d_{VC}(H_1) > 1, but I'd be unsurprised if I were missing something.
I presume he meant it was only one specific point that was being referred to, so \mathcal H_1 is +-- and -++, nothing more
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