Computational Intelligence, SS08
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Intervals

What is the VC-dimension of intervals in $\mathbb{R}$? The target function is specified by an interval, and labels any example positive iff it lies inside that interval.





VC-dim = 2. A set of two points can be shattered, since there's only a single block of positive examples that could lie within the interval. But no set of 3 points can be shattered, because it can not be labeled in alternating +,-,+ order.