小数据集条件下基于不确定先验的BN参数学习

针对以往基于约束的贝叶斯网络（Bayesian networks，BN）参数学习方法在处理先验知识时未考虑知识的不确定性这一缺陷，本文为专家知识附加一个表示不确定性的概率。对所有约束，根据其存在与否生成一个组合，计算该组合的概率，并采用凸优化方法计算该组合条件下的参数估计结果。同时，为加速问题求解，将每个具体的凸优化问题分解为一系列可并行求解的子问题。在得到所有约束组合下的参数之后，依照概率加权思想得到参数估计的最终结果。最后，通过空地战场威胁态势评估模型，证明在参数学习过程中考虑知识的不确定性可有效改善先验知识错误时的BN参数学习效果。

BN parameter learning from small datasets based on uncertain priors

Most of the previous efforts on parameter learning of BN are made ignoring the uncertainty of knowledge. To solve this problem, a probability value is attatched to each expert statement to depicit the uncertainty of the expert knowledge. The weight of each combination of these expert knowlegde is computed and the parameters under this combination are estimated following convex optimization framework. Each of these convex optimization problems is then decomposed into a series of sub problems which can be solved in parallel. Finally, a weighted average is adopted to trade off the estimated result obtained by different combinations. The validity of the proposed approach is verified using a situation assessment model.