Oblivious PAC Learning of Concept Hierarchies

Thomas Dean, Kenneth Basye, Leslie Kaelbling, Evangelos Kokkevis, Oded Maron, Dana Angluin, Sean Engelson

In this paper we introduce an extension of the Probably Approximately Correct (PAC) learning model to study the problem of learning inclusion hierarchies of concepts (sometimes called is-a hierarchies) from random examples. Using only the hypothesis representations output over many different runs of a learning algorithm, we wish to reconstruct the partial order (with respect to generality) among the different target concepts used to train the algorithm. We give an efficient algorithm for this problem with the property that each run is oblivious of all other runs: each run can take place in isolation, without access to any examples except those of the current target concept, and without access to the current pool of hypothesis representations. Thus, additional mechanisms providing shared information between runs are not necessary for the inference of some nontrivial hierarchies.

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