Structure learning of Bayesian networks by continuous particle swarm optimization algorithms

References

• Pearl J. Probabilistic reasoning in intelligent systems: networks of plausible inference. San Francisco (CA): Morgan Kaufmann; 1988.
   Google Scholar
• Neapolitan RE. Learning Bayesian networks. Upper Saddle River (NJ): Prentice Hall; 2004.
   Google Scholar
• Zhang L, Guo H. Introduction to Bayesian networks. Beijing: Science Press; 2006.
   Google Scholar
• Chickering DM. Learning Bayesian networks is NP-complete. In: Fisher D, Lenz HJ, editors. Learning from data. New York: Springer-Verlag; 1996. p. 121–130.
   Google Scholar
• Robinson RW. Counting unlabeled acyclic digraphs. In: Little CHC, editor. Combinatorial mathematics V. Lecture Notes in Statistics, vol. 112. New York: Springer; 1977. p. 28–43.
   Google Scholar
• Cooper GF, Herskovits E. A Bayesian method for the induction of probabilistic networks from data. Mach Learn. 1992;9(4):309–347.
   Web of Science ®Google Scholar
• Alcobé JR. Incremental hill-climbing search applied to Bayesian network structure learning. First International Workshop on Knowledge Discovery in Data Streams; Pisa; 2004.
   Google Scholar
• Cheng J, Greiner R, Kelly J, et al. Learning Bayesian networks from data: an information-theory based approach. Artif Intell. 2002;137(1–2):43–90. doi: 10.1016/S0004-3702(02)00191-1
   Web of Science ®Google Scholar
• Aliferis CF, Statnikov A, Tsamardinos I, et al. Local causal and Markov blanket induction for causal discovery and feature selection for classification part I: algorithms and empirical evaluation. J Mach Learn Res. 2010;11:171–234.
   Web of Science ®Google Scholar
• Brown LE, Tsamardinos I, Aliferis CF. A novel algorithm for scalable and accurate Bayesian network learning. Eleventh World Congress on Medical Informatics; San Francisco; 2004. p. 711–715.
   Google Scholar
• Tsamardinos I, Brown LE, Aliferis CF. The max-min hill-climbing Bayesian network structure learning algorithm. Mach Learn. 2006;65(1):31–78. doi: 10.1007/s10994-006-6889-7
   Web of Science ®Google Scholar
• Larrañaga P, Poza M, Yurramendi Y, et al. Structure learning of Bayesian networks by genetic algorithms: performance analysis of control parameters. IEEE Trans Pattern Anal Mach Intell. 1996;18(9):912–926. doi: 10.1109/34.537345
   Web of Science ®Google Scholar
• Zhang L, Zhang J. Structure learning of BN based on improved genetic algorithm. Comput Syst Appl. 2011;20(9):68–72.
   Google Scholar
• Janžura M, Nielsen J. A simulated annealing-based method for learning Bayesian networks from statistical data. Int J Intell Syst. 2006;21(3):335–348. doi: 10.1002/int.20138
   Web of Science ®Google Scholar
• Wang C, Wang Y. Constrained simulated annealing method for Bayesian network structure learning. J Henan Norm Univ Nat Sci. 2013;41(2):6–9.
   Google Scholar
• Du T, Zhang SS, Wang Z. Efficient learning Bayesian networks using pso. Berlin: Springer Berlin Heidelberg; 2005. p. 151–156. doi: 10.1007/11596448_22
   Google Scholar
• Du T, Zhang S, Wang Z. Learning Bayesian networks from data by particle swarm optimization. J Shanghai Jiaotong Univ Sci. 2006;E-11(4):423–429.
   Google Scholar
• Sahin F, Devasia A. Distributed particle swarm optimization for structural Bayesian network learning. In: Chan FTS, Tiwari MK, editors. Swarm intelligence: focus on ant and particle swarm optimization. Vienna: I-Tech Education and Publishing; 2007. p. 505–532.
   Google Scholar
• Wang T, Yang J. A heuristic method for learning Bayesian networks using discrete particle swarm optimization. Knowl Inf Syst. 2010;24(2):269–281. doi: 10.1007/s10115-009-0239-6
   Web of Science ®Google Scholar
• Wang C, Lü J. Hybrid particle swarm algorithm for learning Bayesian network structure. Sci Technol Rev. 2013;31(22):50–55.
   Google Scholar
• Santos FP, Maciel CD. A PSO approach for learning transition structures of higher-order dynamic Bayesian networks. Biosignals and Biorobotics Conference (2014): Biosignals and Robotics for Better and Safer Living (BRC), 5th ISSNIP-IEEE; Salvador; 2014. p. 1–6.
   Google Scholar
• Schlüter F. A survey on independence-based Markov networks learning. Artif Intell Rev. 2012. Available from: http://link.springer.com/article/10.1007/s10462-012-9346-y
   PubMed Web of Science ®Google Scholar
• Zhang HY, Wang LW, Chen YX. Research progress of probabilistic graphical models: a survey. J Softw. 2013;24(11):2476–2497. doi: 10.3724/SP.J.1001.2013.04486
   Google Scholar
• Liu J, Li H, Luo X. Learning technique of probabilistic graphical models: a review. Acta Automat Sin. 2014;40(6):1025–1044.
   Google Scholar
• Kennedy J, Eberhart RC. Particle swarm optimization. Proceedings of 1995 IEEE International Conference on Neural Networks; Vol. 4; Perth; 1995. p. 1942–1948.
   Google Scholar
• Kennedy J, Eberhart RC. A discrete binary version of the particle swarm algorithm. IEEE International Conference on Systems, Man, and Cybernetics; Vol. 5; Orlando; 1997. p. 4104–4108.
   Google Scholar
• Di RH, Gao XG. Bayesian network structure learning based on restricted particle swarm optimization. Syst Eng Electronics. 2011;33(11):2423–2427.
   Google Scholar
• Heckerman D, Geiger D, Chickering DM. Learning Bayesian networks: the combination of knowledge and statistical data. Mach Learn. 1995;20(3):197–243.
   Web of Science ®Google Scholar
• Schwarz G. Estimating the dimension of a model. Ann Statist. 1978;6(2):461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• Akaike H. Information theory and an extension of the maximum likelihood principle. In: Parzen E, Tanabe K, Kitagawa G, editors. Selected papers of Hirotugu Akaike Springer Series in Statistics (Perspectives in Statistics). New York: Springer; 1998. p. 199–213.
   Google Scholar
• Draper D. Assessment and propagation of model uncertainty (with discussion). J R Stat Soc Ser B. 1995;57(1):45–97.
   Google Scholar
• Rahman MS, King ML. Improved model selection criterion. Comm Stat Simul Comput. 1999;28(1):51–71. doi: 10.1080/03610919908813535
   Web of Science ®Google Scholar
• Lanterman AD. Schwarz, Wallace, and Rissanen: Intertwining themes in theories of model selection. Int Stat Rev. 2001;69(2):185–212. doi: 10.1111/j.1751-5823.2001.tb00456.x
   Web of Science ®Google Scholar
• Rahman MS. Model selection criteria in residual sum of squares form. Int Rev Bus Res Pap. 2010;6(4):501–511.
   Google Scholar
• Heng XC, Qin Z, Wang XH, et al. Research on learning Bayesian networks by particle swarm optimization. Inform Technol J. 2006;5(3):540–545. doi: 10.3923/itj.2006.540.545
   Google Scholar
• Li XL, Wang SC, He XD. Learning Bayesian networks structures based on memory binary particle swarm optimization. In: Wang TD, Li X, Wang X, editors. Simulated evolution and learning. Lecture Notes in Computer Science, vol 4247. Berlin: Springer; 2006. p. 568–574.
   Google Scholar
• Du ZH, Wang YW. A novel structure learning method for constructing gene regulatory network. J Comput Appl. 2009;29(6):1539–1543.
   Google Scholar
• Aouay S, Jamoussi S, BenAyed Y. Particle swarm optimization based method for Bayesian network structure learning. Fifth International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), 2013; Hammamet; 2013. p. 1–6.
   Google Scholar
• de Campos LM. A scoring function for learning Bayesian networks based on mutual information and conditional independence tests. J Mach Learn Res. 2006;7:2149–2187.
   Web of Science ®Google Scholar
• Martínez-Rodríguez AM, May JH, Vargas LG. An optimization-based approach for the design of Bayesian networks. Math Comput Model. 2008;48(7–8):1265–1278. doi: 10.1016/j.mcm.2008.01.007
   Google Scholar
• Lee CP, Leu Y, Yang WN. Constructing gene regulatory networks from microarray data using GA/PSO with DTW. Appl Soft Comput. 2012;12(3):1115–1124. doi: 10.1016/j.asoc.2011.11.013
   Web of Science ®Google Scholar
• Shi Y, Eberhart R A modified particle swarm optimizer. Proceedings of the IEEE International Conference on Evolutionary Computation, Anchorage, AK, USA; IEEE; 1998. p. 69–73
   Google Scholar
• Lepar V, Shenoy PP A comparison of Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer architectures for computing marginals of probability distributions. Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence. San Francisco, CA: Morgan Kaufmann; 1998. p. 328–337
   Google Scholar
• Beinlich IA, Suermondt HJ, Chavez RM, et al. The ALARM monitoring system: a case study with two probabilistic inference techniques for belief networks. In: Second European conference on artificial intelligence in medicine. London: Springer-Verlag; 1989. p. 247–256.
   Google Scholar
• Chickering DM, Meek C. On the incompatibility of faithfulness and monotone DAG faithfulness. Artif Intell. 2006;170(8):653–666. doi: 10.1016/j.artint.2006.03.001
   Web of Science ®Google Scholar
• Poli R, Kennedy J, Blackwell T. Particle swarm optimization – an review. Swarm Intell. 2007;1(1):33–57. doi: 10.1007/s11721-007-0002-0
   Google Scholar
• Bollobás B. Random graphs. 2nd ed. Cambridge: Cambridge University Press; 2001.
   Google Scholar
• Murphy KP. Bayes net toolbox for Matlab. Version: FullBNT-1.0.7; 2007.
   Google Scholar
• Brown G, Pocock A, Zhao MJ, et al. Conditional likelihood maximisation: a unifying framework for information theoretic feature selection. J Mach Learn Res. 2012;13:27–66. (Version: MIToolbox-2.0).
   Web of Science ®Google Scholar
• Pellet JP, Elisseeff A. Using Markov blankets for causal structure learning. J Mach Learn Res. 2008;9:1295–1342.
   Web of Science ®Google Scholar