Uniform characterizations of polynomial-query learnabilities

Authors:
Yosuke Hayashi;Satoshi Matsumoto;Ayumi Shinohara;Masayuki Takeda
Affiliations:
NEC and Department of Informatics, Kyushu University 33, Fukuoka 812-8581, Japan;Department of Mathematical Sciences, Tokai University, Kanagawa 259-1292, Japan;Department of Informatics, Kyushu University 33, Fukuoka 812-8581, Japan;Department of Informatics, Kyushu University 33, Fukuoka 812-8581, Japan
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We consider the exact learning in the query model. We deal with all types of queries introduced by Angluin: membership, equivalence, superset, subset, disjointness and exhaustiveness queries, and their weak (or restricted) versions where no counterexample is returned. For each of all possible combinations of these queries, we uniformly give complete characterizations of boolean concept classes that are learnable using a polynomial number of polynomial-sized queries. Our characterizations show the equivalence between the learnability of a concept class C using queries and the existence of a good query for any subset H of C which is guaranteed to reject a certain fraction of candidate concepts in H regardless of the answer. As a special case for equivalence queries alone, our characterizations directly correspond to the lack of the approximate fingerprint property, which is known to be a sufficient and necessary condition for the learnability using equivalence queries.