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Summary: REVlEW
The Vapnik-Chervonenkis Dimension: Information
versus Complexity in Learning
Yaser S.Abu-Mostafa
California Institute of Terhnohgy, Pasadcna, CA 91125 USA
When feasible, learning is a very attractive alternative to explicit pro-
gramming. This is particularly true in areas where the problems do not
lend themselves to systematic programming, such as pattern recogni-
tion in natural environments. The feasibility of learning an unknown
function from examples depends on two questions:
1. Do the examples convey enough information to determine the
2. Is there a speedy way of constructing the function from the ex-
These questions contrast the roles of information and complexity
in learning. While the two roles share some ground, they are concep-
tually and technically different. In the common language of learning,
the information question is that of generalization and the complex-
ity question is that of scaling. The work of Vapnik and Chervonenkis
(1971)provides the key tools for dealing with the information issue. In
this review, we develop the main ideas of this framework and discuss
how complexity fits in.
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