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Old 05-01-2013, 05:41 AM
Elroch Elroch is offline
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Default Re: Q10 higher bound

Quote:
Originally Posted by jforbes View Post
OK, so if we assume that H is such that it "takes any 1 point and sets it to + or -, with the other points--if any--getting the opposite sign" as proposed by nkatz, then:
for N=1, H={+,-} and shatters this 1 point
for N=2, H={+-,-+} and does not shatter these two points.
for N=3, H={++-, +-+, -++, --+, -+-, +--} and does shatter two points.

What is the VC dimension of this hypothesis set? From the N=2 case, I might conclude that it's 1 (it fails to shatter two points), but from the N=3 case I might conclude it's 2 (it shatters 2 of the points within this set of points). Where am I going wrong?
Unquestionably, the VC-dimensions of the first two hypothesis sets are 1, and that of the third hypothesis set is 2, by the definition.
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