基于单调性约束的离散贝叶斯网络参数学习

Discrete Bayesian network parameter learning based on monotonic constraint

针对小样本条件下的离散贝叶斯网络参数学习问题,提出一种基于单调性约束的学习算法。首先,给出了单调性约束的数学模型,以表达定性的先验信息;然后,将单调性约束以狄利克雷先验的形式集成到贝叶斯估计中,并利用贝叶斯估计进行参数学习;最后,通过仿真实验与最大似然估计和保序回归方法进行比较。实验结果表明,在小样本条件下,所提算法在准确性上优于最大似然估计和保序回归,但时效性介于二者之间。

With respect to the problem of learning parameters of discrete Bayesian network from small sam- ple data, a parameter learning algorithm is proposed based on the monotonic constraint. Firstly, the mathemati- cal model of the monotonic constraint is built to express the qualitative prior information. Then, the monotonic constraint is integrated into the Bayesian estimation as Dirichlet prior and the modified Bayesian estimation is employed to learn parameters. Finally, the proposed algorithm is compared with maximum likelihood estimation and i- sotonic regression by simulation experiments. The experimental results show that the proposed algorithm is better than maximum likelihood estimation and isotonic regression on accuracy, and its＇ timeliness is between the two algorithms.