数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (6): 1767-1784.doi: 10.1016/S0252-9602(13)60122-8

• 论文 • 上一篇    

A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS

Abdelaziz GHRIBI|Afif MASMOUDI   

  1. Laboratory of Physic-Mathematics, University of Sfax, B.P. 1171, Sfax, Tunisia; Laboratory of Probability and Statistics, University of Sfax, B.P. 1171, Sfax, Tunisia
  • 收稿日期:2012-05-12 修回日期:2012-11-03 出版日期:2013-11-20 发布日期:2013-11-20

A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS

Abdelaziz GHRIBI|Afif MASMOUDI   

  1. Laboratory of Physic-Mathematics, University of Sfax, B.P. 1171, Sfax, Tunisia; Laboratory of Probability and Statistics, University of Sfax, B.P. 1171, Sfax, Tunisia
  • Received:2012-05-12 Revised:2012-11-03 Online:2013-11-20 Published:2013-11-20

摘要:

We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the
mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.

关键词: Bayesian network, compound Poisson distribution, multinomial distribution, implicit approach, mobile communication networks

Abstract:

We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the
mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.

Key words: Bayesian network, compound Poisson distribution, multinomial distribution, implicit approach, mobile communication networks

中图分类号: 

  • 46N30