### Abstract

The Bayes coding algorithm for the tree model class is an effective method calculating the prediction probability of appearing symbol at the next time point from the past data under the Bayes criterion. The Bayes optimal prediction is given by the mixture of all models in a given model class, and the Bayes coding algorithm gives an efficient way to calculate a coding probability. This algorithm is applicable to a general prediction problem with Time-series data. Although the Bayes coding algorithm assumes a class of Markov sources, other model classes can be useful for a real prediction problem in practice. For example, the data at the next time point may not always depend on the strict sequence of the past data. It can be possible to construct an efficient Bayes prediction algorithm for a model class on which the probability of the next symbol is conditioned by the cumulative number in a past data sequence. However, there is usually no way to previously know which model class is the best for the observed data sequence. This paper considers the method to mix the prediction probabilities given by the mixtures on different model subclass. If each calculation of the mixtures on subclasses is efficient, the proposed method is also sufficiently efficient. Based on the asymptotic analysis, we evaluate the prediction performance of the proposed method.

Original language | English |
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Title of host publication | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 121-125 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523090 |

Publication status | Published - 2017 Feb 2 |

Event | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 - Monterey, United States Duration: 2016 Oct 30 → 2016 Nov 2 |

### Other

Other | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 |
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Country | United States |

City | Monterey |

Period | 16/10/30 → 16/11/2 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Information Systems
- Signal Processing
- Library and Information Sciences

### Cite this

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016*(pp. 121-125). [7840398] Institute of Electrical and Electronics Engineers Inc..

**A Bayes prediction algorithm for model class composed of several subclasses.** / Goto, Masayuki; Kobayashi, Manabu; Mikawa, Kenta; Hirasawa, Shigeichi.

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

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016.*, 7840398, Institute of Electrical and Electronics Engineers Inc., pp. 121-125, 3rd International Symposium on Information Theory and Its Applications, ISITA 2016, Monterey, United States, 16/10/30.

}

TY - GEN

T1 - A Bayes prediction algorithm for model class composed of several subclasses

AU - Goto, Masayuki

AU - Kobayashi, Manabu

AU - Mikawa, Kenta

AU - Hirasawa, Shigeichi

PY - 2017/2/2

Y1 - 2017/2/2

N2 - The Bayes coding algorithm for the tree model class is an effective method calculating the prediction probability of appearing symbol at the next time point from the past data under the Bayes criterion. The Bayes optimal prediction is given by the mixture of all models in a given model class, and the Bayes coding algorithm gives an efficient way to calculate a coding probability. This algorithm is applicable to a general prediction problem with Time-series data. Although the Bayes coding algorithm assumes a class of Markov sources, other model classes can be useful for a real prediction problem in practice. For example, the data at the next time point may not always depend on the strict sequence of the past data. It can be possible to construct an efficient Bayes prediction algorithm for a model class on which the probability of the next symbol is conditioned by the cumulative number in a past data sequence. However, there is usually no way to previously know which model class is the best for the observed data sequence. This paper considers the method to mix the prediction probabilities given by the mixtures on different model subclass. If each calculation of the mixtures on subclasses is efficient, the proposed method is also sufficiently efficient. Based on the asymptotic analysis, we evaluate the prediction performance of the proposed method.

AB - The Bayes coding algorithm for the tree model class is an effective method calculating the prediction probability of appearing symbol at the next time point from the past data under the Bayes criterion. The Bayes optimal prediction is given by the mixture of all models in a given model class, and the Bayes coding algorithm gives an efficient way to calculate a coding probability. This algorithm is applicable to a general prediction problem with Time-series data. Although the Bayes coding algorithm assumes a class of Markov sources, other model classes can be useful for a real prediction problem in practice. For example, the data at the next time point may not always depend on the strict sequence of the past data. It can be possible to construct an efficient Bayes prediction algorithm for a model class on which the probability of the next symbol is conditioned by the cumulative number in a past data sequence. However, there is usually no way to previously know which model class is the best for the observed data sequence. This paper considers the method to mix the prediction probabilities given by the mixtures on different model subclass. If each calculation of the mixtures on subclasses is efficient, the proposed method is also sufficiently efficient. Based on the asymptotic analysis, we evaluate the prediction performance of the proposed method.

UR - http://www.scopus.com/inward/record.url?scp=85015170656&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015170656&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85015170656

SP - 121

EP - 125

BT - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -