Shattering All Sets of K Points in 'General Position' Requires (k - 1)/2 Parameters

NeCo 1997 pp. 337-348

doi:10.1162/NECO.1997.9.2.337 /neco/1997/sontag1997neco-shattering/

Abstract

For classes of concepts defined by certain classes of analytic functions depending on n parameters, there are nonempty open sets of samples of length 2n + 2 that cannot be shattered. A slighly weaker result is also proved for piecewise-analytic functions. The special case of neural networks is discussed.

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Cite

Text

Sontag. "Shattering All Sets of K Points in 'General Position' Requires (k - 1)/2 Parameters." Neural Computation, 1997. doi:10.1162/NECO.1997.9.2.337

Markdown

[Sontag. "Shattering All Sets of K Points in 'General Position' Requires (k - 1)/2 Parameters." Neural Computation, 1997.](https://mlanthology.org/neco/1997/sontag1997neco-shattering/) doi:10.1162/NECO.1997.9.2.337

BibTeX

@article{sontag1997neco-shattering,
  title     = {{Shattering All Sets of K Points in 'General Position' Requires (k - 1)/2 Parameters}},
  author    = {Sontag, Eduardo D.},
  journal   = {Neural Computation},
  year      = {1997},
  pages     = {337-348},
  doi       = {10.1162/NECO.1997.9.2.337},
  volume    = {9},
  url       = {https://mlanthology.org/neco/1997/sontag1997neco-shattering/}
}