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.
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Shvaytser, H. A Necessary Condition for Learning from Positive Examples. Machine Learning 5, 101–113 (1990). https://doi.org/10.1023/A:1022663809420
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DOI: https://doi.org/10.1023/A:1022663809420