小数据集条件下贝叶斯网络自适应参数学习方法

Learning Bayesian network parameters from small data set: an adaptive method

中文关键词  贝叶斯网络  小数据集  参数估计  凸优化  自适应方法

英文关键词  Bayesian networks  small data set  parameter estimation  convex optimization  adaptive method

中文摘要

      针对小数据集条件下贝叶斯网络参数学习问题, 约束最大似然(CML)和定性最大后验概率(QMAP)方法是 两种约束适用性较好的方法. 当样本数量、约束数量、参数位置不同时, 上述两种方法互有优劣, 进而导致方法上的 难以选择. 因此, 本文提出一种自适应参数学习方法: 首先, 利用CML和QMAP方法学习得到两组参数; 然后, 基于 拒绝–接受采样和空间最大后验概率思想自定义计算得到样本权重、约束权重、参数位置权重; 最后, 基于上述参数 和权重计算得到新的参数解. 实验表明: 在任何条件下, 本文方法计算得到参数的精度接近甚至优于CML和 QMAP方法的最优解.

英文摘要

      For parameter learning of Bayesian networks from small data set, constrained maximum likelihood (CML) method and qualitative maximum a posterior (QMAP) method are two approaches, which suit all types of existing parameter constraints. However, those two approaches dominate each other when samples size, constraint number or true-parameter location varies. That makes it tough to choose between those two methods. For that reason, a novel adaptive parameter learning method is proposed in this paper. First, CML method and QMAP method are employed to learn BN parameters. Then, sample weight, constraint weight, and parameter-location weight are defined and calculated based on rejectionacceptance sampling and spatial maximum a posterior analysis. Finally, a new set of parameters are calculated as the weighted values of CML and QMAP solutions. Furthermore, simulation results reveal that precision of parameters learnt by the proposed method, in any cases, approaches and even outperforms those of CML method and QMAP method.