Bayesian network structure learning with improved genetic algorithm

International Journal of Intelligent SystemsVolume 37, Issue 9 p. 6023-6047 RESEARCH ARTICLE Bayesian network structure learning with improved genetic algorithm Baodan Sun, Baodan Sun Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, ChinaSearch for more papers by this authorYun Zhou, Corresponding Author Yun Zhou [email protected] orcid.org/0000-0001-7328-0275 Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, China Correspondence Yun Zhou, Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, China. Email: [email protected]Search for more papers by this author Baodan Sun, Baodan Sun Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, ChinaSearch for more papers by this authorYun Zhou, Corresponding Author Yun Zhou [email protected] orcid.org/0000-0001-7328-0275 Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, China Correspondence Yun Zhou, Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, China. Email: [email protected]Search for more papers by this author First published: 03 February 2022 https://doi.org/10.1002/int.22833Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract As an important model of machine learning, Bayesian networks (BNs) have received a lot of attentions since they can be used for classification via probabilistic inference. However, since it is a complicated combination optimization problem, BN structure learning cannot be solved with classic convex optimization algorithms. Hence, evolutionary algorithms provide an alternative way to find a global solution to BN structure learning problem. In this paper, we improve the biased random-key genetic algorithm to solve the BN structure learning problem. Meanwhile, we apply a local optimization model as its decoder to improve the performance of the proposed algorithm. Finally, we conduct our experiments on nine benchmark networks and a real dataset of cross-site scripting (XSS) attack. Experimental results show that the proposed algorithm can obtain more accurate solutions than other state-of-the-art algorithms and achieve a good performance in XSS attack detection for web security. REFERENCES 1Grüttemeier N, Komusiewicz C. Learning Bayesian networks under sparsity constraints: a parameterized complexity analysis. In: Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence, Vol. 7; 2020: 4217-4223. 2Gu J, Zhou Q. Learning big Gaussian Bayesian networks: partition, estimation and fusion. J Mach Learn Res. 2020; ​ 21. 3de Campos CP, Ji Q. Properties of Bayesian dirichlet scores to learn Bayesian network structures. In: Twenty-Fourth AAAI Conference on Artificial Intelligence 2010. Atlanta, GA; 2010. 4Bartlett M, Cussens J. Integer linear programming for the Bayesian network structure learning problem. Artif Intell. 2017; 244: 258-271. 5Hongru L, Huiping G. A hybrid structure learning algorithm for Bayesian network using experts' knowledge. Entropy. 2018; 20(8): 620. 6Oyen D, Lane T. Bayesian discovery of multiple Bayesian networks via transfer learning. In: 2013 IEEE 13th International Conference on Data Mining; 2013: 577-586. 7Yu Y, Chen J, Gao T, Yu M. DAG-GNN: DAG structure learning with graph neural networks. In: International Conference on Machine Learning (ICML); 2019. 8Correia AHC, Cussens J, de Campos C. On pruning for score-based Bayesian network structure learning. In: Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research, Vol. 108. PMLR; Aug 26-28, 2020: 2709-2718. 9Chu VW, Wong RK, Chen F, Fong S, Hung PC. Self-regularized causal structure discovery for trajectory-based networks. J Comput Syst Sci. 2016; 82(4): 594-609. 10Yu K, Wu X, Ding W, Wang H. Exploring causal relationships with streaming features*. Comput J. 2012; 55(9): 1103-1117. doi:10.1093/comjnl/bxs032 11Jin Z, Li J, Liu L, Le TD, Sun B, Wang R. Discovery of causal rules using partial association. In: 2012 IEEE 12th International Conference on Data Mining; 2012:309-318. doi:10.1109/ICDM.2012.36 12Hong Y, Liu Z, Mai G. An efficient algorithm for large-scale causal discovery. Soft Comput. 2017; 21(24): 7381-7391. 13Ma S, Li J, Liu L, Le TD. Mining combined causes in large data sets. Knowl-Based Syst. 2016; 92: 104-111. 14Khanteymoori AR, Olyaee MH, Abbaszadeh O, Valian M. A novel method for Bayesian networks structure learning based on breeding swarm algorithm. Soft Comput. 22(9): 3049-3060. 15Junzhong J, Cuicui Y, Jiming L, Jinduo L, Baocai Y. A comparative study on swarm intelligence for structure learning of Bayesian networks. Soft Comput. 2016; 21(22): 1-26. 16Ji J, Wei H, Liu C. An artificial bee colony algorithm for learning Bayesian networks. Soft Comput. 2013; 17(6): 983-994. 17Yang C, Ji J, Liu J, Liu J, Yin B. Structural learning of Bayesian networks by bacterial foraging optimization. Int J Approx Reason. 2016; 69: 147-167. 18Campos L, Fernández-Luna J, Gámez J, Puerta JM. Ant colony optimization for learning Bayesian networks. Int J Approx Reason. 2002; 31(3): 291-311. 19Zhang Q, Li Z, Zhou CJ, Wei XP. Bayesian network structure learning based on the chaotic particle swarm optimization algorithm. Genetics Mol Res. 2013; 12(4): 4468-4479. 20Wang J, Liu S. A novel discrete particle swarm optimization algorithm for solving Bayesian network structures learning problem. Int J Comput Math. 2019; 96: 1-23. 21Gheisari S, Meybodi MR. BNC-PSO: structure learning of Bayesian networks by Particle Swarm Optimization. Inform Sci. 2016; 348: 272-289. 22Fukuda S, Yoshihiro T. Learning Bayesian networks using probability vectors. Adv Intell Syst Comput. 2014; 290: 503-510. 23Lee J, Chung W, Kim E, Kim S. A new genetic approach for structure learning of Bayesian networks: matrix genetic algorithm. Int J Control Autom Syst. 2010; 8(2): 398-407. 24Vafaee F. Learning the structure of large-scale Bayesian networks using genetic algorithm. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation. GECCO'14, Association for Computing Machinery, New York, NY; 2014: 855-862. 25Khanteymoori AR, Menhaj MB, Homayounpour MM. Structure learning in Bayesian networks using asexual reproduction optimization. Etri J. 2011; 33(1): 39-49. 26Carvalho A. A cooperative coevolutionary genetic algorithm for learning Bayesian network structures. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. GECCO'11, Association for Computing Machinery, New York, NY; 2011: 1131-1138. 27Shetty S, Song M. Structure learning of Bayesian networks using a semantic genetic algorithm-based approach. In: ITRE 2005. 3rd International Conference on Information Technology: Research and Education; 2005: 454-458. 28Baioletti M, Milani A, Santucci V. Learning Bayesian networks with algebraic differential evolution. In: Parallel Problem Solving from Nature. Springer International Publishing; 2018: 436-448. 29Constantinou AC. Learning Bayesian networks with the Saiyan algorithm. ACM Trans Knowl Discov Data. 2020; 14(4): 44. 30Gonçalves J, Almeida J. A hybrid genetic algorithm for assembly line balancing. J Heuristics. 2002; 8: 629-642. 31Sun B, Zhou Y. Biased random-key genetic algorithm for structure learning. In: 12th International Conference on Advances in Swarm Intelligence, ICSI 2021. Vol. 12689 LNCS; 2021: 399-411. 32Goldberg DE. Genetic algorithms in search, optimization and machine learning. 1st ed. Addison-Wesley Longman Publishing Co., Inc.; 1989. 33Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of ICNN'95—International Conference on Neural Networks. Vol. 4; 1995: 1942-1948. 34David MC, Christopher M, David H. Large-sample learning of bayesian networks is NP-hard. J Mach Learn Res. 2004; 5(1999): 1287-1330. 35Bean JC. Genetic algorithms and random keys for sequencing and optimization. Orsa J Comput. 1994; 6: 154-160. 36Fernando J, Mauricio G. Biased random-key genetic algorithms for combinatorial optimization. J Heuristics. 2011; 17(5): 487-525. 37Zheng X, Aragam B, Ravikumar P, Xing EP. DAGs with NO TEARS: Continuous optimization for structure learning. In: Advances in Neural Information Processing Systems; 2018: 9472-9483. 38Byrd RH, Lu P, Nocedal J, Zhu C. A limited memory algorithm for bound constrained optimization. Siam J Scientific Comput. 1995; 16(5): 1190-1208. 39Wei D, Gao T, Yu Y. DAGs with no fears: a closer look at continuous optimizationfor learning Bayesian networks. In: Advances in Neural Information Processing Systems; 2020: 3895-3906. 40Constantinou AC. Evaluating structure learning algorithms with a balanced scoring function. CoRR. 2019;abs/1905.12666. 41Zhou Y, Wang P. An ensemble learning approach for XSS attack detection with domain knowledge and threat intelligence. Comput Security. 2019; 82(May): 261-269. Citing Literature Volume37, Issue9September 2022Pages 6023-6047 ReferencesRelatedInformation