### Abstract

The CTW(Context Tree Weighting) algorithm is an efficient universal coding algorithm on context tree models. The CTW algorithm has been interpreted as the non-predictive Bayes coding algorithm assuming a special prior distribution over context tree models. An efficient recursive calculation method using a gathering context tree in the CTWalgorithm is well known. Although there exist efficient recursive algorithms for the Bayes codes assuming a special class of prior distributions, the basic property ofthe prior distribution class has been scarcely investigated. In this paper we show the exact definition of a prior distribution class on context tree models that has the similar property to the class of conjugate priors. We show the posterior distribution is also included in the same distribution class as the prior distribution class. So we can also construct an efficient algorithm ofpredictive Bayes codes on context tree models by using the prior distribution class. Lastly the asymptotic mean code length of the codes IS investigated.

Original language | English |
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Title of host publication | ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology |

Pages | 938-941 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2007 |

Event | ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology - Cairo Duration: 2007 Dec 15 → 2007 Dec 18 |

### Other

Other | ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology |
---|---|

City | Cairo |

Period | 07/12/15 → 07/12/18 |

### Fingerprint

### Keywords

- Bayes universal codes
- Context tree models
- Prior distribution
- Source coding

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Information Systems
- Signal Processing

### Cite this

*ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology*(pp. 938-941). [4458049] https://doi.org/10.1109/ISSPIT.2007.4458049

**A class of prior distributions on context tree models and an efficient algorithm of the Bayes codes assuming it.** / Matsushima, Toshiyasu; Hirasawa, Shigeich.

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

*ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology.*, 4458049, pp. 938-941, ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology, Cairo, 07/12/15. https://doi.org/10.1109/ISSPIT.2007.4458049

}

TY - GEN

T1 - A class of prior distributions on context tree models and an efficient algorithm of the Bayes codes assuming it

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeich

PY - 2007

Y1 - 2007

N2 - The CTW(Context Tree Weighting) algorithm is an efficient universal coding algorithm on context tree models. The CTW algorithm has been interpreted as the non-predictive Bayes coding algorithm assuming a special prior distribution over context tree models. An efficient recursive calculation method using a gathering context tree in the CTWalgorithm is well known. Although there exist efficient recursive algorithms for the Bayes codes assuming a special class of prior distributions, the basic property ofthe prior distribution class has been scarcely investigated. In this paper we show the exact definition of a prior distribution class on context tree models that has the similar property to the class of conjugate priors. We show the posterior distribution is also included in the same distribution class as the prior distribution class. So we can also construct an efficient algorithm ofpredictive Bayes codes on context tree models by using the prior distribution class. Lastly the asymptotic mean code length of the codes IS investigated.

AB - The CTW(Context Tree Weighting) algorithm is an efficient universal coding algorithm on context tree models. The CTW algorithm has been interpreted as the non-predictive Bayes coding algorithm assuming a special prior distribution over context tree models. An efficient recursive calculation method using a gathering context tree in the CTWalgorithm is well known. Although there exist efficient recursive algorithms for the Bayes codes assuming a special class of prior distributions, the basic property ofthe prior distribution class has been scarcely investigated. In this paper we show the exact definition of a prior distribution class on context tree models that has the similar property to the class of conjugate priors. We show the posterior distribution is also included in the same distribution class as the prior distribution class. So we can also construct an efficient algorithm ofpredictive Bayes codes on context tree models by using the prior distribution class. Lastly the asymptotic mean code length of the codes IS investigated.

KW - Bayes universal codes

KW - Context tree models

KW - Prior distribution

KW - Source coding

UR - http://www.scopus.com/inward/record.url?scp=71549170873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71549170873&partnerID=8YFLogxK

U2 - 10.1109/ISSPIT.2007.4458049

DO - 10.1109/ISSPIT.2007.4458049

M3 - Conference contribution

AN - SCOPUS:71549170873

SN - 9781424418350

SP - 938

EP - 941

BT - ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology

ER -