A Necessary Condition for Learning from Positive Examples

Authors:
Haim Shvaytser
Affiliations:
David Sarnoff Research Center, CN-5300, Princeton, NJ 08543-5300. HAIM%SARNOFF@PRINCETON.EDU
Venue:
Machine Learning
Year:
1990

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Abstract

We present a simple combinatorial criterion for determining concept classes that cannot be learned in the sense of Valiant from a polynomial number of positive-only examples. The criterion is applied to several types of Boolean formulae in conjunctive and disjunctive normal form, to the majority function, to graphs with large connected components, and to a neural network with a single threshold unit. All are shown to be nonlearnable from positive-only examples.