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 - 2007/12/1

Y1 - 2007/12/1

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

T3 - ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology

SP - 938

EP - 941

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

T2 - ISSPIT 2007 - 2007 IEEE International Symposium on Signal Processing and Information Technology

Y2 - 15 December 2007 through 18 December 2007

ER -