摘要
针对小样本数据集下学习贝叶斯网络(Bayesian networks,BN)结构的不足,以及随着条件集的增大,利用统计方法进行条件独立(Conditional independence,CI)测试不稳定等问题,提出了一种基于先验节点序学习网络结构的优化方法.新方法通过定义优化目标函数和可行域空间,首次将贝叶斯网络结构学习问题转化为求解目标函数极值的数学规划问题,并给出最优解的存在性及唯一性证明,为贝叶斯网络的不断扩展研究提出了新的方案.理论证明以及实验结果显示了新方法的正确性和有效性.
To solve the drawbacks of learning Bayesian networks (BN) from small data set and the unreliability of the conditional independence (CI) tests when the conditioning sets become too large,this paper proposes an optimization approach for structural learning Bayesian networks based on prior node ordering. It is the first time that a problem of structural learning for a Bayesian network is transformed into its related mathematical programming problem by defining objective function and feasible region. And,we have proved the existence and uniqueness of the numerical solution. The approach offers a new opinion for the research of extended Bayesian networks. Theoretical and experimental results show that the new approach is correct and effective.
出处
《自动化学报》
EI
CSCD
北大核心
2011年第12期1514-1519,共6页
Acta Automatica Sinica
基金
国家自然科学基金(60974082
61075055)
国家杰出青年科学基金项目(11001214)
西安电子科技大学基本科研业务基金项目(K50510700004)资助~~
关键词
贝叶斯网络
优化模型
条件独立测试
结构学习
节点序
Bayesian network (BN)
optimization model
conditional independence test
structure learning
node ordering