Maximising entropy on the nonparametric predictive inference model for multinomial data

被引：27

作者：

Abellan, Joaquin ^{[1
]}

Baker, Rebecca M. ^{[2
]}

Coolen, Frank P. A. ^{[2
]}

机构：

[1] Univ Granada, Dept Comp Sci & Artificial Intelligence, Granada, Spain

[2] Univ Durham, Dept Math Sci, Durham, England

来源：

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH | 2011年 / 212卷 / 01期

关键词：

Entropy maximization; Imprecise probabilities; Nonparametric predictive inference; Uncertainty measures; IMPRECISE DIRICHLET MODEL; DEMPSTER-SHAFER THEORY; TOTAL UNCERTAINTY; LOWER PROBABILITIES; INFORMATION-THEORY;

D O I：

10.1016/j.ejor.2011.01.020

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

摘要：

The combination of mathematical models and uncertainty measures can be applied in the area of data mining for diverse objectives with as final aim to support decision making. The maximum entropy function is an excellent measure of uncertainty when the information is represented by a mathematical model based on imprecise probabilities. In this paper, we present algorithms to obtain the maximum entropy value when the information available is represented by a new model based on imprecise probabilities: the nonparametric predictive inference model for multinomial data (NPI-M), which represents a type of entropy-linear program. To reduce the complexity of the model, we prove that the NPI-M lower and upper probabilities for any general event can be expressed as a combination of the lower and upper probabilities for the singleton events, and that this model can not be associated with a closed polyhedral set of probabilities. An algorithm to obtain the maximum entropy probability distribution on the set associated with NPI-M is presented. We also consider a model which uses the closed and convex set of probability distributions generated by the NPI-M singleton probabilities, a closed polyhedral set. We call this model A-NPI-M. A-NPI-M can be seen as an approximation of NPI-M, this approximation being simpler to use because it is not necessary to consider the set of constraints associated with the exact model. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：112 / 122

页数：11

共 44 条

[11]

[Anonymous], 1988, Bayesian statistics

[12]

[Anonymous], 1992, Fuzzy measure theory

[13]

[Anonymous], 2000, Fuzzy measures and integrals: theory and applications

[14] Nonparametric predictive inference and interval probability [J].