On the sample complexity of consistent learning with one-sided error

Eiji Takimoto; Akira Maruoka

doi:10.1007/3-540-57370-4_53

On the sample complexity of consistent learning with one-sided error

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

Abstract

Although consistent learning is sufficient for PAC-learning, it has not been found what strategy makes learning more efficient, especially on the sample complexity, i.e., the number of examples required. For the first step towards this problem, only classes that have consistent learning algorithms with one-sided error are considered. A combinatorial quantity called maximal particle sets is introduced, and an upper bound of the sample complexity of consistent learning with one-sided error is obtained in terms of maximal particle sets. For the class of n-dimensional parallel axis rectangles, one of those classes that are consistently learnable with one-sided error, the cardinality of the maximal particle set is estimated and (Formula Found) upper bound of the learning algorithm for the class is obtained. This bound improves the bounds due to Blumer et al. [2] and meets the lower bound within a constant factor.

Original language	English
Title of host publication	Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings
Editors	Klaus P. Jantke, Shigenobu Kobayashi, Etsuji Tomita, Takashi Yokomori
Publisher	Springer Verlag
Pages	265-278
Number of pages	14
ISBN (Print)	9783540573708
DOIs	https://doi.org/10.1007/3-540-57370-4_53
Publication status	Published - Jan 1 1993
Externally published	Yes
Event	4th Workshop on Algorithmic Learning Theory, ALT 1993 - Tokyo, Japan Duration: Nov 8 1993 → Nov 10 1993

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	744 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th Workshop on Algorithmic Learning Theory, ALT 1993
Country	Japan
City	Tokyo
Period	11/8/93 → 11/10/93

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-57370-4_53

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Cite this

Takimoto, E., & Maruoka, A. (1993). On the sample complexity of consistent learning with one-sided error. In K. P. Jantke, S. Kobayashi, E. Tomita, & T. Yokomori (Eds.), Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings (pp. 265-278). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 744 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57370-4_53

On the sample complexity of consistent learning with one-sided error. / Takimoto, Eiji; Maruoka, Akira.

Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. ed. / Klaus P. Jantke; Shigenobu Kobayashi; Etsuji Tomita; Takashi Yokomori. Springer Verlag, 1993. p. 265-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 744 LNAI).

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

Takimoto, E & Maruoka, A 1993, On the sample complexity of consistent learning with one-sided error. in KP Jantke, S Kobayashi, E Tomita & T Yokomori (eds), Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 744 LNAI, Springer Verlag, pp. 265-278, 4th Workshop on Algorithmic Learning Theory, ALT 1993, Tokyo, Japan, 11/8/93. https://doi.org/10.1007/3-540-57370-4_53

Takimoto E, Maruoka A. On the sample complexity of consistent learning with one-sided error. In Jantke KP, Kobayashi S, Tomita E, Yokomori T, editors, Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. Springer Verlag. 1993. p. 265-278. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-57370-4_53

Takimoto, Eiji ; Maruoka, Akira. / On the sample complexity of consistent learning with one-sided error. Algorithmic Learning Theory - 4th International Workshop, ALT 1993, Proceedings. editor / Klaus P. Jantke ; Shigenobu Kobayashi ; Etsuji Tomita ; Takashi Yokomori. Springer Verlag, 1993. pp. 265-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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