利用先验正态分布的贝叶斯网络参数学习

针对贝叶斯网络参数的近似等式约束,提出采用正态分布构建该类约束的数学模型;然后用Dirichlet分布逼近正态分布,并通过目标优化计算Dirichlet分布的超参数;最后采用贝叶斯最大后验概率(maximum a posterior,MAP)估计方法计算网络参数值。在不同样本量的数据集下进行实验测试,将本文方法与其他4种主要方法进行比较,结果表明:该方法的参数学习精度都好于其他4种方法,尤其是在样本量较小的情况下。该方法的运行时间高于其他4种方法,但相同样本量的数据集下,学习精度的提高倍数要高于时间增加的倍数。

Learning Bayesian networks parameters by prior knowledge of normal distribution

For the approximate equality constraint of Bayesian networks parameters, a normal distribution model is proposed. Then, Dirichlet distribution is utilized to approximate the normal distribution. And the super parameters of Dirichlet distribution are calculated by target optimization. Finally, Bayesian maximum a posterior (MAP) estimation is employed to estimate the parameters of Bayesian networks. With data sets of different sizes, the proposed method is compared with the other four main methods. The experiments results show that the parameter learning accuracy of the proposed method are better than the other four methods, especially in the case of small sample size. And the run time is greater than the other four methods. However, the multiplier of learning accuracy is higher than the multiplier of time increase under the condition of the same sample size.