A Block Learning Algorithm With Improved K-means Algorithm for Learning Sparse BN Optimal Structure
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摘要: 目前贝叶斯网络(Bayesian networks, BN)的传统结构学习算法在处理高维数据时呈现出计算负担过大、在合理时间内难以得到期望精度结果的问题.为了在高维数据下学习稀疏BN的最优结构, 本文提出了一种学习稀疏BN最优结构的改进K均值分块学习算法.该算法采用分而治之的策略, 首先采用互信息作为节点间距离度量, 利用融合互信息的改进K均值算法对网络分块; 其次, 使用MMPC (Max-min parent and children)算法得到整个网络的架构, 根据架构找到块间所有边的可能连接方向, 从而找到所有可能的图结构; 之后, 对所有图结构依次进行结构学习; 最终利用评分找到最优BN.实验证明, 相比现有分块结构学习算法, 本文提出的算法不仅习得了网络的精确结构, 且学习速度有一定提高; 相比非分块经典结构学习算法, 本文提出的算法在保证精度基础上, 学习速度大幅提高, 解决了非分块经典结构学习算法无法在合理时间内处理高维数据的难题.Abstract: At present, the traditional structure learning algorithm of Bayesian networks (BN) shows the problem of excessive computational burden and difficulty in obtaining the desired accuracy in a reasonable time when processing high-dimensional data. In order to learn the optimal structure of sparse BN under high-dimensional data, this paper proposes a block learning algorithm with improved K-means algorithm for learning sparse BN optimal structure. The algorithm adopts the strategy of divide and conquer. Firstly, we use mutual information as the distance between nodes, and the improved K-means algorithm with mutual information is used to block the network. Secondly, the MMPC algorithm is used to obtain the skeleton of the whole network. According to the skeleton, the possible connection directions of all edges between the blocks are found, so that all possible graph structures are found; after that, structural learning is performed sequentially for all possible graph structures; finally, the best BN is found by using scoring function. Experiments show that compared with the existing block structure learning algorithm, the proposed algorithm not only learns the optimal structure of the network, but also improves the learning speed definitely. Compared with the non-blocking classical structure learning algorithm, the learning speed of the algorithm proposed in this paper is greatly improved on the basis of ensuring accuracy, which solves the problem that the traditional algorithms cannot process high-dimensional data in a reasonable time.
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Key words:
- Bayesian network (BN) /
- structure learning /
- improved K-means algorithm /
- block learning
1) 本文责任编委 胡清华 -
图 11 OS-IKM算法与现有分块算法的运行时间对比
Fig. 11 The comparison of the run time between OS-IKM algorithm and other block algorithms
图 12 OS-IKM算法与其他非分块经典结构学习算法的运行时间对比
Fig. 12 The comparison of the run time between OS-IKM algorithm and other traditional algorithms
表 1 实验中用到的BN的参数
Table 1 Details of Bayesian networks in the experiments
网络 节点数 边数 Sachs 11 17 Mybnet1 18 27 Boerlage92 23 36 Insurance 27 52 Mybnet2 32 42 Alarm 37 46 
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表 2 汉明距离对比
Table 2 The Hamming distances of the seven algorithms
OS-IKM算法 OS-FN算法 SAR算法 MMHC based on graph partitioning算法 GS based on graph partitioning算法 动态规划算法 HC算法 (a) Sachs网络 $A(N_G^\ast)$ 0 0 0 0 0 1 1 $M(N_G^\ast)$ 3 3 0 3 3 0 0 $I(N_G^\ast)$ 4 3 2 6 6 3 4 $H(N_G^\ast)$ 7 6 2 9 9 4 5 (b) Mybnet1网络 $A(N_G^\ast)$ 0 0 0 0 0 3 4 $M(N_G^\ast)$ 2 3 1 2 2 2 2 $I(N_G^\ast)$ 6 8 3 6 11 12 6 $H(N_G^\ast)$ 8 11 4 8 13 17 12 (c) Boerlage92网络 $A(N_G^\ast)$ 0 0 3 0 0 7 0 $M(N_G^\ast)$ 9 9 6 10 9 3 10 $I(N_G^\ast)$ 5 7 7 8 8 8 9 $H(N_G^\ast)$ 14 16 16 18 17 18 19 (d) Mybnet2网络 $A(N_G^\ast)$ 0 0 1 0 0 – 0 $M(N_G^\ast)$ 5 6 5 7 7 – 8 $I(N_G^\ast)$ 9 9 9 11 9 – 6 $H(N_G^\ast)$ 14 15 15 18 16 – 14 (e) Alarm网络 $A(N_G^\ast)$ 0 0 7 0 0 – 8 $M(N_G^\ast)$ 9 11 4 8 11 – 5 $I(N_G^\ast)$ 6 8 4 14 9 – 12 $H(N_G^\ast)$ 15 19 15 22 20 – 25
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表 3 BIC评分对比($\times 10^4$)
Table 3 The BIC scores of the seven algorithms ($\times 10^4$)
OS-IKM算法 OS-FN算法 MMHC based on Graph Partitioning算法 GS based on Graph Partitioning算法 动态规划算法 HC算法 Sachs $-3.7004$ $-3.7907$ $-3.7038$ $-3.7813$ $-3.6616$ $-3.6753$ Mybnet1 $-5.0766$ $-5.0823$ $-5.0833$ $-5.0853$ $-5.0946$ $-5.0773$ Boerlage92 $-5.0474$ $-5.0754$ $-5.0853$ $-5.0773$ $-5.065$ $-5.0758$ Mybnet2 $-9.1036$ $-9.1300$ $-9.1478$ $-9.1459$ – $-9.0947$ Alarm $-6.521$ $-6.7179$ $-6.7889$ $-6.7486$ – $-6.8439$
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[1] Peal J. Probabilistic Reasoning in Intelligent Systems. Massachusetts: Morgan Kaufmann, 1988. [2] Soli R, Kaabi B, Barhoumi M, Maktouf C, Ahmed S. Bayesian phylogenetic analysis of the influenza-A virus genomes isolated in Tunisia and determination of potential recombination events. Molecular Phylogenetics And Evolution, 2019, 134: 253-268 doi: 10.1016/j.ympev.2019.01.019 [3] Stahl E A, Wegmann D, Trynka G, Gutierrez-Achury J, Do R, Voight B F, et al. Bayesian inference analyses of the polygenic architecture of rheumatoid arthritis. Nature Genetics, 2012, 44(5): 483-489 doi: 10.1038/ng.2232 [4] Ehsani-Moghaddam B, Queenan J A, MacKenzie J, Birtwhistle R V. Mucopolysaccharidosis type Ⅱ detection by naive Bayes classifier: An example of patient classification for a rare disease using electronic medical records from the Canadian Primary Care Sentinel Surveillance Network. Plos One, 2018, 13(12): e0209018 doi: 10.1371/journal.pone.0209018 [5] 郑文博, 王坤峰, 王飞跃.基于贝叶斯生成对抗网络的背景消减算法.自动化学报, 2018, 44(5): 878-890 doi: 10.16383/j.aas.2018.c170562Zheng Wen-Bo, Wang Kun-Feng, Wang Fei-Yue. Background subtraction algorithm with bayesian generative adversarial networks. Acta Automatica Sinica, 2018, 44(5): 878-890 doi: 10.16383/j.aas.2018.c170562 [6] 顾晓清, 蒋亦樟, 王士同.用于不平衡数据分类的0阶TSK型模糊系统.自动化学报, 2017, 43(10): 1773-1788 doi: 10.16383/j.aas.2017.c160200Gu Xiao-Qing, Jiang Yi-Zhang, Wang Shi-Tong. Zero-order TSK-type fuzzy system for imbalanced data classiflcation. Acta Automatica Sinica, 2017, 43(10): 1773-1788 doi: 10.16383/j.aas.2017.c160200 [7] 王松涛, 周真, 曲寒冰, 李彬. RGB-D图像的贝叶斯显著性检测.自动化学报, 2017, 43(10): 1810-1828 doi: 10.16383/j.aas.2017.e160141Wang Song-Tao, Zhou Zhen, Qu Han-Bing, Li Bin. Bayesian saliency detection for RGB-D images. Acta Automatica Sinica, 2017, 43(10): 1810-1828 doi: 10.16383/j.aas.2017.e160141 [8] 韩绍金, 李建勋.基于密度核估计的贝叶斯网络结构学习算法.计算机工程与应用, 2014, 50(15): 107-112 doi: 10.3778/j.issn.1002-8331.1307-0003Han Shao-Jin, Li Jian-Xun. Structure learning algorithm for bayesian network based on probability density kernel estimation. Computer Engineering & Applications, 2014, 50(15): 107-112 doi: 10.3778/j.issn.1002-8331.1307-0003 [9] Malone B, Yuan C, Hansen E A. Memory-efficient dynamic programming for learning optimal bayesian networks. In: Proceedings of the Twenty-Fifth Association for the Advance of Artificial Intelligence Conference. AAAI Press, 2011. 1057-1062 [10] Yuan C, Malone B. Learning optimal bayesian networks: a shortest path perspective. Journal of Artificial Intelligence Research, 2013, 48: 23-65 doi: 10.1613/jair.4039 [11] Bartlett M, Cussens J. Integer linear programming for the bayesian network structure learning problem. Artificial Intelligence, 2017, 244: 258-271 doi: 10.1016/j.artint.2015.03.003 [12] Singh A P, Moore A W. Finding optimal bayesian networks by dynamic programming. Technical Report CMU-CALD-05-106, School of Computer Science, Carnegie Mellon University, USA, 2005. [13] Koller D, Friedman N. Probabilistic Graphical Models. Cambridge, MA: MIT Press, 2009. [14] Li S H, Zhang J, Huang K H, Gao C X. A graph partitioning approach for bayesian network structure learning. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014 [15] Liu H, Zhou S G, Lam W, Guan J H. A new hybrid method for learning Bayesian networks: separation and reunion. Knowledge-Based Systems, 2017, 121: 185-197 doi: 10.1016/j.knosys.2017.01.029 [16] Newman M E J, Girvan M. Finding and evaluating community structure in networks. Physical Review E, 2004, 69(2): 026113 doi: 10.1103/PhysRevE.69.026113 [17] Newman M E J. Modularity and community structure in networks. In: Proceedings of the 2006 American Physical Society March Meeting. American Physical Society, 2006. 8577-8582 [18] Zhang W, Zhang G X, Chen X H, Liu Y Q, Zhou X M, Zhou J L. DHC: a distributed hierarchical clustering algorithm for large datasets. Journal of Circuits, Systems and Computers, 2019, 28(4): 1950065.1-1950065.26 http://d.old.wanfangdata.com.cn/Periodical/dzkjdxxb201705020 [19] Zhou Zhi-Hua. Machine Learning. Tsinghua University Press, 2016. [20] Birant D, Kut A. ST-DBSCAN: an algorithm for clustering spatial-temporal data. Data and Knowledge Engineering, 2007, 60(1): 208-221 http://d.old.wanfangdata.com.cn/Periodical/xddzjs201921029 [21] Viswanath P, Pinkesh R. I-DBSCAN: a fast hybrid density based clustering method. In: Proceedings of IEEE 18th International Conference on Pattern Recognition International Conference on Pattern Recognition. Hong Kong, China: IEEE Computer Society, 2006. 912-915 [22] Newman M E J. Fast algorithm for detecting community structure in networks. Phys Rev E Stat Nonlin Soft Matter Phys, 2004, 69(6): 066133. doi: 10.1103/PhysRevE.69.066133 [23] Vinh N X, Chetty M, Coppel R, Wangikar P P. GlobalMIT: learning globally optimal dynamic bayesian network with the mutual information test criterion. Bioinformatics, 2011, 27(19): 2765-2766 doi: 10.1093/bioinformatics/btr457 [24] Konstantinos T, Vincenzo L, Sofia T, Tsamardinos I. On scoring maximal ancestral graphs with the max-min hill climbing algorithm. International Journal of Approximate Reasoning, 2018 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0d5df1ec3afbd3527a261d532e769283 [25] Tsamardinos I. The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 2006, 65(1): 31-78 doi: 10.1007-s10994-006-6889-7/ -
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