基于拓扑序和惩罚似然的贝叶斯网络结构学习

Bayesian Network Structure Learning Based on Topological Order and Penalty Likelihood

  • 摘要: 基于连续优化的学习方法,提出了一种基于节点拓扑序和惩罚似然的贝叶斯网络结构估计算法(NOE-MLE 算法). 该方法第一阶段通过最小二乘损失以及最大无圈子图进行节点序的估计, 第二阶段基于估计出的节点序, 对DAG的加权邻接矩阵上三角部分进行估计, 使用基于自适应Lasso的极大似然函数学习贝叶斯网络结构. 借助数值实验,将该方法与已有连续优化方法进行了比较, 结果表明该方法在保证了精度的同时, 可以在更短的时间内完成网络结构学习.

     

    Abstract: With the aid of continuous optimization, this work proposes a novel Bayesian network structure learning algorithm, named Bayesian network structural learning algorithm based on node topological ordering and the regularized likelihood estimation (NOE-MLE, in abbreviation). The first stage of this algorithm estimates the topological order of nodes through the least square loss and the maximum acyclic subgraph. While for the second stage, the triangular part of the weighted adjacency matrix of a model structure is estimated. By comparing with the existing structural learning methods based on continuous optimization techniques, numerical experiments show that the proposed algorithm can complete the network structure learning in a shorter time while ensuring the accuracy.

     

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