On approximately identifying concept classes in the limit

Satoshi Kobayashi, Takashi Yokomori

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Citations (Scopus)

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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages298-312
Number of pages15
Volume997
ISBN (Print)3540604545, 9783540604549
Publication statusPublished - 1995
Externally publishedYes
Event6th International Workshop on Algorithmic Learning Theory, ALT 1995 - Fukuoka, Japan
Duration: 1995 Oct 181995 Oct 20

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume997
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Workshop on Algorithmic Learning Theory, ALT 1995
CountryJapan
CityFukuoka
Period95/10/1895/10/20

Fingerprint

Identifiability
Topology
Quasi-order
Upper Approximation
Closure Properties
Characterization Theorem
Best Approximation
Union
Intersection
Concepts
Class
Target
Approximation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Kobayashi, S., & Yokomori, T. (1995). On approximately identifying concept classes in the limit. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 997 Springer Verlag, 1995. p. 298-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 997).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kobayashi, S & Yokomori, T 1995, On approximately identifying concept classes in the limit. in 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.
Kobayashi S, Yokomori T. On approximately identifying concept classes in the limit. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 997. Springer Verlag. 1995. p. 298-312. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Kobayashi, Satoshi ; Yokomori, Takashi. / On approximately identifying concept classes in the limit. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 997 Springer Verlag, 1995. pp. 298-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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