Learning from examples with unspecified attribute values

We introduce the UAV learning model in which some of the attributes in the examples are unspecified. In our model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classificatoin given to x is "?" (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns an example x (that could have unspecified attributes) for which h(x) is incorrect. We show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the MQ and UAV-EQ oracles as long as the counterexamples provided by the UAV-EQ oracle have a logarithmic number of unspecified attributes. We also show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the UAV-MQ and UAV-EQ oracles as well as an oracle... Read complete abstract on page 2.