### 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.

Original language | English |
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Title of host publication | Discovery Science - 1st International Conference, DS 1998, Proceedings |

Editors | Setsuo Arikawa, Hiroshi Motoda |

Publisher | Springer Verlag |

Pages | 84-92 |

Number of pages | 9 |

ISBN (Print) | 3540653902, 9783540653905 |

Publication status | Published - Jan 1 1998 |

Event | 1st International Conference on Discovery Science, DS 1998 - Fukuoka, Japan Duration: Dec 14 1998 → Dec 16 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1532 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st International Conference on Discovery Science, DS 1998 |
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Country | Japan |

City | Fukuoka |

Period | 12/14/98 → 12/16/98 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Discovery Science - 1st International Conference, DS 1998, Proceedings*(pp. 84-92). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1532). Springer Verlag.

**Uniform characterizations of Polynomial-Query learnabilities.** / Hayashi, Yosuke; Matsumoto, Satoshi; Shinohara, Ayumi; Takeda, Masayuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Discovery Science - 1st International Conference, DS 1998, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1532, Springer Verlag, pp. 84-92, 1st International Conference on Discovery Science, DS 1998, Fukuoka, Japan, 12/14/98.

}

TY - GEN

T1 - Uniform characterizations of Polynomial-Query learnabilities

AU - Hayashi, Yosuke

AU - Matsumoto, Satoshi

AU - Shinohara, Ayumi

AU - Takeda, Masayuki

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=84949211417&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84949211417

SN - 3540653902

SN - 9783540653905

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 84

EP - 92

BT - Discovery Science - 1st International Conference, DS 1998, Proceedings

A2 - Arikawa, Setsuo

A2 - Motoda, Hiroshi

PB - Springer Verlag

ER -