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Bayesian network structure training based on a game of learning automata

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Abstract

Bayesian network (BN) is a probabilistic graphical model which describes the joint probability distribution over a set of random variables. Finding an optimal network structure based on an available training dataset is one of the most important challenges in the field of BNs. Since the problem of searching the optimal BN structure belongs to the class of NP-hard problems, typically greedy algorithms are used to solve it. In this paper two novel learning automata-based algorithms are proposed to solve the BNs’ structure learning problem. In both, there is a learning automaton corresponding with each possible edge to determine the appearance and the direction of that edge in the constructed network; therefore, we have a game of learning automata, at each stage of the proposed algorithms. Two special cases of the game of the learning automata have been discussed, namely, the game with a common payoff and the competitive game. In the former, all the automata in the game receive a unique payoff from the environment, but in the latter, each automaton receives its own payoff. As the algorithms proceed, the learning processes focus on the BN structures with higher scores. The use of learning automata has led to design the algorithms with a guided search scheme, which can avoid getting stuck in local maxima. Experimental results show that the proposed algorithms are capable of finding the optimal structure of BN in an acceptable execution time; and compared with other search-based methods, they outperform them.

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References

  1. Larranaga P, Poza M, Yarramendi Y, Murga RH, Kuijpers CMH (1996) Learning of Bayesian networks by genetic algorithms: a performance analysis of control parameters. IEEE Trans Pattern Anal Mach Intell 18:912–926

    Article  Google Scholar 

  2. Cheng J, Bell DA, Liu W (1997) An algorithm for Bayesian belief network construction from Data. In: Proceedings of AI & STAT’97, pp 83–90

  3. Larranaga P, Kuijpers CMH, Murga RH, Yurramendi Y (1996) Learning Bayesian network structures by searching for the best ordering with genetic algorithms. IEEE Trans Syst Man Cybern 26:487–493

    Article  Google Scholar 

  4. Myers JW, Laskey KB, Levitt TS (1999) Learning Bayesian networks from incomplete data with stochastic search algorithms. In: UAI Conference, pp 476–485

  5. Rezvani N, Meybodi MR (2009) A learning automata-based technique for training Bayesian networks. In: Proceeding of international conference CACTE, pp 201–212

  6. Tsamardinos I, Brown LE, Aliferis CF (2006) The max-min hill-climbing Bayesian Network structure learning algorithm. Mach Learn 65:31–78

    Article  Google Scholar 

  7. Heckerman D (1995) Learning with Bayesian networks. In: ICML’95

  8. Murphy KP (2001) An introduction to graphical models. Technical Report, Intel Research Technical Report.

  9. Lam W, Bacchus F (1994) Learning Bayesian belief networks: an approach based on the MDL principle. Elsevier Comput Intell 10:269–293

    Article  Google Scholar 

  10. Gallagher M, Wood I, Keith J (2007) Bayesian inference in estimation of distribution algorithms. In: Proceeding of the IEEE congress on evolutionary computation, pp 127–133.

  11. Chickering DM, Geiger D, Heckerman D (1994) Learning Bayesian network is NP-hard. Technical report MSR-TR-94-14

  12. Heckerman D, Geiger D, Chickering DM (2008) A tutorial on learning with Bayesian networks, innovations in Bayesian networks, chapter 3. Springer, Berlin, pp 33–82

    Google Scholar 

  13. Ahn CW, Ramakrishna RS (2008) On the scalability of real-coded Bayesian optimization algorithm. IEEE Trans Evol Comut 12:307–322

    Article  Google Scholar 

  14. Ahn CW, Ramakrishna RS, Goldberg DE (2004) Real-coded Bayesian optimization algorithm: bringing the strength of BOA into the continuous world. Lect Notes Comput Sci 3102:840–851

    Article  Google Scholar 

  15. Heckerman D, Geiger D, Chickering DM (1995) Learning Bayesian networks: the combination of knowledge and statistical data. Technical Report MSR-TR-94-09.

  16. Ahn CW (2006) Advances in evolutionary algorithms: theory, design and practice, studies in computational intelligence. Springer, Berlin

    Google Scholar 

  17. Thathachar MAL, Sastry PS (2002) Varieties of learning automata: an overview. IEEE Trans Syst Man Cybern 32:711–722

    Article  Google Scholar 

  18. Narendra KS, Thathachar MAL (1989) Learning automata: an introduction. Prentice-Hall, Inc., Upper Saddle River

    MATH  Google Scholar 

  19. Beigy H, Meybodi MR (2006) A new continuous action-set learning automata for function optimization. J Franklin Inst 343:27

    Article  MathSciNet  MATH  Google Scholar 

  20. Santharam G, Sastry PS, Thathachar MAL (1994) Continuous action set learning automata for stochastic optimization. J Franklin Inst 331B:607–628

    Article  MathSciNet  MATH  Google Scholar 

  21. Oommen BJ, Roberts TD (2000) Continuous learning automata solutions to the capacity assignment problem. IEEE Trans Comput 49:608–620

    Article  Google Scholar 

  22. Najim K, Poznyak AS (1994) Learning automata: theory and applications. Pergamon Press, Inc., Elmsford

    MATH  Google Scholar 

  23. Obaidat MS, Papadimitriou GI, Pomportsis AS, Laskaridis HS (2002) Learning automata-based bus arbitration for shared-medium ATM switches. IEEE Trans Syst Man Cybern 32:815–820

    Article  Google Scholar 

  24. Papadimitriou GI, Obaidat MS, Pomportsis AS (2002) On the use of learning automata in the control of broad-cast networks: a methodology. IEEE Trans Syst Man Cybern 32:781–790

    Article  Google Scholar 

  25. Beigy H, Meybodi MR (2009) Cellular learning automata based dynamic channel assignment algorithms. Int J Comput Intell Appl 8(3):287–314

    Article  MATH  Google Scholar 

  26. Beigy H, Meybodi MR (2006) Utilizing distributed learning automata to solve stochastic shortest path problems. Int J Uncertain Fuzz Knowl Based Syst 14:591–615

    Article  MathSciNet  MATH  Google Scholar 

  27. Granmo OC, Oommen BJ, Myrer SA, Olsen MG (2007) Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation. IEEE Trans Syst Man Cybern 37:166–175

    Article  Google Scholar 

  28. Beigy H, Meybodi MR (2009) Adaptive limited fractional guard channel algorithms a learning automata approach. Int J Uncertain Fuzz Knowl Based Syst 17(6):881–913

    Article  MATH  Google Scholar 

  29. Beigy H, Meybodi MR (2009) A learning automata-based algorithm for determination of the number of hidden units for three layer neural networks. Int J Syst Sci 40:101–118

    Article  MATH  Google Scholar 

  30. Sastry PS, Nagendra GD, Manwani N (2010) A team of continuous-action learning automata for noisetolerant learning of half-spaces. IEEE Trans Syst Man Cybern 40:19–28

    Article  Google Scholar 

  31. Oommen BJ, Hashem MK (2010) Modeling a student classroom interaction in a tutorial-like system using learning automata. IEEE Trans Syst Man Cybern 40:29–42

    Article  MATH  Google Scholar 

  32. Kamil Amir (2003) Graph algorithms CS61B. Spring, UC Berkeley

    Google Scholar 

  33. Sastry PS, Phansalkar VV, Thathachar MAL (1994) Decentralized learning of nash equilibria in multi-person stochastic games with incomplete information. IEEE Trans Syst Man Cybern 24:769–777

    Article  MathSciNet  Google Scholar 

  34. Beinlich IA, Suermondt HJ, Chavez RM, Cooper GF (1989) The ALARM monitoring system: a case study with two probabilistic inference techniques for belief networks. In: Proceedings of second european conference on artificial intelligence, pp 247–256

  35. Herskovits EH (1991) Computer Based Probabilistic Network Construction. Doctoral dissertation, Medical Information Sciences, Stanford University.

  36. Campos De, Luis M, Fernandez-Luna JM, Gámez JA, Puerta JM (2002) Ant colony optimization for learning Bayesian networks. Int J Approx Reason 31(3):291–311

    Article  MathSciNet  MATH  Google Scholar 

  37. Yuan C, Malone B, Wu X (2011) Learning optimal Bayesian networks using A* search. In: IJCAI proceedings-international joint conference on artificial intelligence, vol. 22, no. 3, p 2186.

  38. Singh AP, Moore AW (2005) Finding optimal Bayesian networks by dynamic programming. Technical Report, Carnegie Mellon University

  39. Cussens J, Bartlett M (2013) Advances in Bayesian network learning using integer programming. arXiv preprint arXiv:1309.6825

  40. Jaakkola T, Sontag D, Globerson A, Meila M (2010) Learning Bayesian network structure using LP relaxations. In: Proceedings of the international conference on artificial intelligence and statistics, pp 358–365

  41. Wang XZ, He YL, Wang DD (2014) Non-naive Bayesian classifiers for classification problems with continuous attributes. IEEE Trans Cybern 44(1):21–39

    Article  Google Scholar 

  42. He Yulin, Wang Ran, Kwong Sam, Wang Xizhao (2014) Bayesian classifiers based on probability density estimation and their applications to simultaneous fault diagnosis. Inf Sci 259:252–268

    Article  MathSciNet  MATH  Google Scholar 

  43. Feng G, Zhang JD, Liao SS (2014) A novel method for combining Bayesian networks, theoretical analysis, and its applications. Pattern Recogn 47(5):2057–2069

    Article  MATH  Google Scholar 

  44. Murphy PM, Aha DW (1995) UCI repository of machine learning databases. http://www.ics.uci.edu/~mlearn/MLRepository.html

  45. Kohavi R, John G (1997) Wrappers for feature subset selection. Elsevier Sci Artif Intell 97:273–324

    Article  MATH  Google Scholar 

  46. Pernkopf F (2005) Bayesian network classifiers versus selective k-NN classifier. Pattern Recogn 38(1):1–10

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer, Science and Research Branch, Islamic Azad University, Tehran, Iran

    S. Gheisari

  2. Computer Engineering and Information Technology Department, Amirkabir University of Technology, Tehran, Iran

    M. R. Meybodi, M. Dehghan & M. M. Ebadzadeh

Authors
  1. S. Gheisari
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  2. M. R. Meybodi
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  3. M. Dehghan
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  4. M. M. Ebadzadeh
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Corresponding author

Correspondence to S. Gheisari.

Appendix A: Experiments implementation

Appendix A: Experiments implementation

In order to evaluate the performance of proposed algorithms and compare them with other algorithms, required programs are implemented with C# on.Net Framework. We have implemented two main elements called DataModel and BayesModel. In DataModel preprocess of datasets is done and an object oriented model is used to maintain the datasets. BayesModel constructs a BN based on a given dataset and then evaluates it. Figures 6 and 7 represent their class diagram.

Fig. 6
figure 6

DataModel class diagram

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Fig. 7
figure 7

BayesModel class diagram

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Gheisari, S., Meybodi, M.R., Dehghan, M. et al. Bayesian network structure training based on a game of learning automata. Int. J. Mach. Learn. & Cyber. 8, 1093–1105 (2017). https://doi.org/10.1007/s13042-015-0476-9

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  • DOI: https://doi.org/10.1007/s13042-015-0476-9

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