Lower Bound on VC-Dimension by Local Shattering
暂无分享,去创建一个
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.
[1] Eduardo D. Sontag,et al. Neural Networks with Quadratic VC Dimension , 1995, J. Comput. Syst. Sci..
[2] Dittert,et al. Correction to "Lower Bounds for Sorting with Realistic Instruction Sets" , 1986 .
[3] Peter L. Bartlett,et al. Correction to Lower Bounds on VC-Dimension of Smoothly Parameterized Function Classes1 , 1997, Neural Computation.
[4] Eduardo D. Sontag,et al. Feedforward Nets for Interpolation and Classification , 1992, J. Comput. Syst. Sci..