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Published March 1993 | Published
Journal Article Open

Hints and the VC Dimension


Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also derive a new quantity that defines a VC dimension for the hint itself. This quantity is used to estimate the number of examples needed to "absorb" the hint. We carry out the analysis for two types of hints, invariances and catalysts. We also describe how the same method can be applied to other types of hints.

Additional Information

© 1993 The MIT Press. Received 21 April 1992; accepted 15 July 1992. This work was supported by AFOSR Grant 92-J-0398 and the Feynman-Hughes fellowship. The author wishes to thank Dr. Demetri Psaltis for a number of useful comments.

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