### 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, 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 axis-parallel rectangles, one of those classes that are consistently learnable with one-sided error, the cardinality of the maximal particle set is estimated and O(d/ε+1/ε log 1/δ) upper bound of the learning algorithm for the class is obtained. This bound improves the bounds due to Blumer et al. and meets the lower bound within a constant factor.

Original language | English |
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Pages (from-to) | 518-525 |

Number of pages | 8 |

Journal | IEICE Transactions on Information and Systems |

Volume | E78-D |

Issue number | 5 |

Publication status | Published - May 1 1995 |

Externally published | Yes |

Event | Proceedings of the IEICE Transaction on Information and Systems - Tokyo, Jpn Duration: Nov 1 1993 → Nov 1 1993 |

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### All Science Journal Classification (ASJC) codes

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

### Cite this

*IEICE Transactions on Information and Systems*,

*E78-D*(5), 518-525.

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

Research output: Contribution to journal › Conference article

*IEICE Transactions on Information and Systems*, vol. E78-D, no. 5, pp. 518-525.

}

TY - JOUR

T1 - On the sample complexity of consistent learning with one-sided error

AU - Takimoto, Eiji

AU - Maruoka, Akira

PY - 1995/5/1

Y1 - 1995/5/1

N2 - 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, 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 axis-parallel rectangles, one of those classes that are consistently learnable with one-sided error, the cardinality of the maximal particle set is estimated and O(d/ε+1/ε log 1/δ) upper bound of the learning algorithm for the class is obtained. This bound improves the bounds due to Blumer et al. and meets the lower bound within a constant factor.

AB - 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, 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 axis-parallel rectangles, one of those classes that are consistently learnable with one-sided error, the cardinality of the maximal particle set is estimated and O(d/ε+1/ε log 1/δ) upper bound of the learning algorithm for the class is obtained. This bound improves the bounds due to Blumer et al. and meets the lower bound within a constant factor.

UR - http://www.scopus.com/inward/record.url?scp=0029309351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029309351&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0029309351

VL - E78-D

SP - 518

EP - 525

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 5

ER -