Hints and the VC dimension

  • Authors:
  • Yaser S. Abu-Mostafa

  • Affiliations:
  • -

  • Venue:
  • Neural Computation
  • Year:
  • 1993

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Abstract

Learning from hints is a generalization of learning fromexamples that allows for a variety of information about the unknownfunction to be used in the learning process. In this paper, we usethe VC dimension, an established tool for analyzing learning fromexamples, to analyze learning from hints. In particular, we showhow the VC dimension is affected by the introduction of a hint. Wealso derive a new quantity that defines a VC dimension for the hintitself. This quantity is used to estimate the number of examplesneeded to "absorb" the hint. We carry out the analysis for twotypes of hints, invariances and catalysts. We also describe how thesame method can be applied to other types of hints.