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Neural Computation, Vol 9, 771-776, Copyright © 1997 by The MIT Press

NOTES

Lower Bound on VC-Dimension by Local Shattering

Yossi Erlich, Dan Chazan, Scott Petrack and Avi Levi

We show that the VC-dimension of a smoothly parameterized function class is not less than the dimension of any manifold in the parameter space, as long as distinct parameter values induce distinct decision boundaries. A similar theorem was published recently and used to introduce lower bounds on VC-dimension for several cases (Lee, Bartlett, & Williamson, 1995). This theorem is not correct, but our theorem could replace it for those cases and many other practical ones.


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Copyright © 1997 by The MIT Press.