### Abstract

The problem of learning a concept from examples in the model introduced by Valiant is discussed. According to the traditional ways of thinking, it is assumed that the learnability is independent of the occurrence probability of instance. By utilizing this probability, we propose the metric as a new measure to determine the complexity of hypothesis space. The metric measures the hardness of discrimination between hypotheses. Furthermore, we obtain the average metric dependent on prior information. This metric is the measure of complexity for hypothesis space in the average. Similarly in the worst case, we obtain the minimum metric. We make clear the relationship between these measures and the Vapnik - Chervonenkis (VC) dimension. Finally, we show the upper bound on sample complexity utilizing the metric. This results can be applied in the discussion on the learnability of the class with an infinite VC dimension.

Original language | English |
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Title of host publication | Proceedings of the IEEE International Conference on Systems, Man and Cybernetics |

Publisher | IEEE |

Pages | 132-137 |

Number of pages | 6 |

Volume | 1 |

Publication status | Published - 1994 |

Event | Proceedings of the 1994 IEEE International Conference on Systems, Man and Cybernetics. Part 1 (of 3) - San Antonio, TX, USA Duration: 1994 Oct 2 → 1994 Oct 5 |

### Other

Other | Proceedings of the 1994 IEEE International Conference on Systems, Man and Cybernetics. Part 1 (of 3) |
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City | San Antonio, TX, USA |

Period | 94/10/2 → 94/10/5 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics*(Vol. 1, pp. 132-137). IEEE.

**On the complexity of hypothesis space and the sample complexity for machine learning.** / Nakazawa, Makoto; Kohnosu, Toshiyuki; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

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

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics.*vol. 1, IEEE, pp. 132-137, Proceedings of the 1994 IEEE International Conference on Systems, Man and Cybernetics. Part 1 (of 3), San Antonio, TX, USA, 94/10/2.

}

TY - GEN

T1 - On the complexity of hypothesis space and the sample complexity for machine learning

AU - Nakazawa, Makoto

AU - Kohnosu, Toshiyuki

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 1994

Y1 - 1994

N2 - The problem of learning a concept from examples in the model introduced by Valiant is discussed. According to the traditional ways of thinking, it is assumed that the learnability is independent of the occurrence probability of instance. By utilizing this probability, we propose the metric as a new measure to determine the complexity of hypothesis space. The metric measures the hardness of discrimination between hypotheses. Furthermore, we obtain the average metric dependent on prior information. This metric is the measure of complexity for hypothesis space in the average. Similarly in the worst case, we obtain the minimum metric. We make clear the relationship between these measures and the Vapnik - Chervonenkis (VC) dimension. Finally, we show the upper bound on sample complexity utilizing the metric. This results can be applied in the discussion on the learnability of the class with an infinite VC dimension.

AB - The problem of learning a concept from examples in the model introduced by Valiant is discussed. According to the traditional ways of thinking, it is assumed that the learnability is independent of the occurrence probability of instance. By utilizing this probability, we propose the metric as a new measure to determine the complexity of hypothesis space. The metric measures the hardness of discrimination between hypotheses. Furthermore, we obtain the average metric dependent on prior information. This metric is the measure of complexity for hypothesis space in the average. Similarly in the worst case, we obtain the minimum metric. We make clear the relationship between these measures and the Vapnik - Chervonenkis (VC) dimension. Finally, we show the upper bound on sample complexity utilizing the metric. This results can be applied in the discussion on the learnability of the class with an infinite VC dimension.

UR - http://www.scopus.com/inward/record.url?scp=0028726019&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028726019&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0028726019

VL - 1

SP - 132

EP - 137

BT - Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

PB - IEEE

ER -