Learning from Incomplete Boundary

We consider learnability with membership queries in the presence of incomplete information. In the incomplete boundary query model introduced by Blum et al. 7], it is assumed that membership queries on instances near the boundary of the target concept may receive a \don't know" answer. We show that zero{one threshold functions are eeciently learnable in this model. The learning algorithm uses split graphs when the boundary region has radius 1, and their generalization to split hypergraphs (for which we give a split-nding algorithm) when the boundary region has constant radius greater than 1. We use a notion of indistinguishability of concepts that is appropriate for this model.