一种贝叶斯网络结构学习的混合随机抽样算法

A Hybrid Stochastic Sampling Algorithm for Bayesian Network Structure Learning

贝叶斯网络结构学习的随机抽样算法存在收敛速度慢的问题,为此,结合均匀抽样和独立抽样,从初始样本、抽样方式和建议分布3个方面对抽样过程进行改进,提出一种混合型马尔可夫链蒙特卡罗抽样算法(HSMHS)。基于节点之间的互信息生成网络结构的初始样本,在迭代抽样阶段,按一定的概率随机选择均匀抽样和独立抽样,并根据当前抽样的样本总体计算独立抽样的建议分布,以改善抽样过程的融合性,加快收敛速度。对算法进行正确性分析,证明其抽样过程收敛于网络结构的后验概率分布,可保持较高的学习精度。在标准数据集上的实验结果表明,HSMHS算法的学习效率和精度均高于同类算法MHS、PopMCMC和Order-MCMC。

According to slow convergence speed of stochastic sampling algorithm, based on uniform sampler and independent sampler, by improving convergence speed from the initial sample, sampling method and proposal distribution, a hybrid markov chain Monte Carlo sampling algorithm（HSMHS） is put forward in this paper. Based on mutual information between network nodes, it generates initial samples of network structure. In iteration sampling phase, according to certain probability distribution, it randomly selects uniform sampler or independent sampler, and computs proposal distribution of independent sampler based on the current samples to improve the mixing of sampling process. It can be proved that sampling process of HSMHS converges to the posterior probability of network structure, and the algorithm has a good learning accuracy. Experimental results on standard data set also verify that both learning efficiency and precision of HSMHS outperform classical algorithms MHS, PopMCMC and Order-MCMC.