### Abstract

In this paper, we introduce various kinds of approximations of a concept and propose a framework of approximate learning in case that a target concept could be outside the hypothesis space. We present some characterization theorems for approximately identifiability. In particular, we show a remarkable result that the upper-best approximate identifiability from complete data is collapsed into the upper-best approximate identifiability from positive data. Further, some other characterizations for approximate identifiability from positive data are presented, where we establish a relationship between approximate identifiability and some important notions in quasi-order theory and topology theory. The results obtained in this paper are essentially related to the closure property of concept classes under infinite intersections (or infinite unions). We also show that there exist some interesting example concept classes with such properties (including specialized EFS’s) by which an upper-best approximation of any concept can be identifiable in the limit from positive data.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 298-312 |

Number of pages | 15 |

Volume | 997 |

ISBN (Print) | 3540604545, 9783540604549 |

Publication status | Published - 1995 |

Externally published | Yes |

Event | 6th International Workshop on Algorithmic Learning Theory, ALT 1995 - Fukuoka, Japan Duration: 1995 Oct 18 → 1995 Oct 20 |

### Publication series

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

Volume | 997 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Workshop on Algorithmic Learning Theory, ALT 1995 |
---|---|

Country | Japan |

City | Fukuoka |

Period | 95/10/18 → 95/10/20 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 997, pp. 298-312). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 997). Springer Verlag.

**On approximately identifying concept classes in the limit.** / Kobayashi, Satoshi; Yokomori, Takashi.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 997, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 997, Springer Verlag, pp. 298-312, 6th International Workshop on Algorithmic Learning Theory, ALT 1995, Fukuoka, Japan, 95/10/18.

}

TY - GEN

T1 - On approximately identifying concept classes in the limit

AU - Kobayashi, Satoshi

AU - Yokomori, Takashi

PY - 1995

Y1 - 1995

N2 - In this paper, we introduce various kinds of approximations of a concept and propose a framework of approximate learning in case that a target concept could be outside the hypothesis space. We present some characterization theorems for approximately identifiability. In particular, we show a remarkable result that the upper-best approximate identifiability from complete data is collapsed into the upper-best approximate identifiability from positive data. Further, some other characterizations for approximate identifiability from positive data are presented, where we establish a relationship between approximate identifiability and some important notions in quasi-order theory and topology theory. The results obtained in this paper are essentially related to the closure property of concept classes under infinite intersections (or infinite unions). We also show that there exist some interesting example concept classes with such properties (including specialized EFS’s) by which an upper-best approximation of any concept can be identifiable in the limit from positive data.

AB - In this paper, we introduce various kinds of approximations of a concept and propose a framework of approximate learning in case that a target concept could be outside the hypothesis space. We present some characterization theorems for approximately identifiability. In particular, we show a remarkable result that the upper-best approximate identifiability from complete data is collapsed into the upper-best approximate identifiability from positive data. Further, some other characterizations for approximate identifiability from positive data are presented, where we establish a relationship between approximate identifiability and some important notions in quasi-order theory and topology theory. The results obtained in this paper are essentially related to the closure property of concept classes under infinite intersections (or infinite unions). We also show that there exist some interesting example concept classes with such properties (including specialized EFS’s) by which an upper-best approximation of any concept can be identifiable in the limit from positive data.

UR - http://www.scopus.com/inward/record.url?scp=84941155929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941155929&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540604545

SN - 9783540604549

VL - 997

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

SP - 298

EP - 312

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

PB - Springer Verlag

ER -