TY - GEN

T1 - On approximately identifying concept classes in the limit

AU - Kobayashi, Satoshi

AU - Yokomori, Takashi

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1995.

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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U2 - 10.1007/3-540-60454-5_47

DO - 10.1007/3-540-60454-5_47

M3 - Conference contribution

AN - SCOPUS:84941155929

SN - 3540604545

SN - 9783540604549

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

SP - 298

EP - 312

BT - Algorithmic Learning Theory - 6th International Workshop, ALT 1995, Proceedings

A2 - Jantke, Klaus P.

A2 - Shinohara, Takeshi

A2 - Zeugmann, Thomas

PB - Springer Verlag

T2 - 6th International Workshop on Algorithmic Learning Theory, ALT 1995

Y2 - 18 October 1995 through 20 October 1995

ER -