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 |
|---|---|
| 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
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 proceeding › Conference contribution
}
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.
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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 -