The IBMAP approach for Markov network structure learning

  • Federico Schlüter
  • Facundo Bromberg
  • Alejandro Edera


In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum.


Markov network Structure learning Independence tests Knowledge discovery EDAs 

Mathematics Subject Classifications (2010)



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)Google Scholar
  2. 2.
    Agresti, A.: Categorical Data Analysis, 2nd edn. Wiley (2002)Google Scholar
  3. 3.
    Alden, M.: MARLEDA: Effective Distribution Estimation Through Markov Random Fields. Ph.D. thesis, Dept of CS University of Texas Austin (2007)Google Scholar
  4. 4.
    Aliferis, C., Statnikov, A., Tsamardinos, I., Mani, S., Koutsoukos, X.: Local Causal and Markov Blanket induction for causal discovery and feature selection for classification part i: algorithms and empirical evaluation. JMLR 11, 171–234 (2010)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Aliferis, C., Statnikov, A., Tsamardinos, I., Mani, S., Koutsoukos, X.: Local causal and Markov blanket induction for causal discovery and feature selection for classification part ii: analysis and extensions. JMLR 11, 235–284 (2010)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Aliferis, C., Tsamardinos, I., Statnikov, A.: HITON, a novel Markov blanket algorithm for optimal variable selection. AMIA Fall (2003)Google Scholar
  7. 7.
    Bromberg, F., Margaritis, D.: Improving the reliability of causal discovery from small data sets using argumentation. JMLR 10, 301–340 (2009)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Bromberg, F., Margaritis, D., Honavar, V.: Efficient markov network structure discovery using independence tests. In: Proc SIAM Data Mining, p. 06 (2006)Google Scholar
  9. 9.
    Bromberg, F., Margaritis, D., Honavar, V.: Efficient Markov network structure discovery using independence tests. JAIR 35, 449–485 (2009)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Chickering, D.M.: Learning Bayesian networks is NP-Complete. In: Fisher, D., Lenz, H. (eds.) Learning from Data: Artificial Intelligence and Statistics V, pp. 121–130. Springer, Berlin (1996)Google Scholar
  11. 11.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)CrossRefzbMATHGoogle Scholar
  12. 12.
    Davis, J., Domingos, P.: Bottom-up learning of Markov network structure. In: ICML, pp. 271–278 (2010)Google Scholar
  13. 13.
    Della Pietra, S., Della Pietra, V.J., Lafferty, J.D.: Inducing features of random fields. IEEE Trans. PAMI 19(4), 380–393 (1997)CrossRefGoogle Scholar
  14. 14.
    Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using Bayesian networks to analyze expression data. J. Comput. Biol., 601–620 (2000)Google Scholar
  15. 15.
    Ganapathi, V., Vickrey, D., Duchi, J., Koller, D.: Constrained approximate maximum entropy learning of Markov random fields. In: Uncertainty in Artificial Intelligence, pp. 196–203 (2008)Google Scholar
  16. 16.
    Hammersley, J.M., Clifford, P.: Markov fields on finite graphs and lattices (1968)Google Scholar
  17. 17.
    Hettich, S., Bay, S.D. The UCI KDD archive (1999)Google Scholar
  18. 18.
    Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)Google Scholar
  19. 19.
    Larraṅaga, P., Lozano, J.A.: Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Kluwer, Norwell (2002)CrossRefGoogle Scholar
  20. 20.
    Lauritzen, S.L.: Graphical Models. Oxford University Press, New York (1996)Google Scholar
  21. 21.
    Lee, S.I., Ganapathi, V., Koller, D.: Efficient structure learning of Markov networks using L1-regularization. NIPS (2006)Google Scholar
  22. 22.
    Li, S.: Markov Random Field Modeling in Image Analysis. Springer (2009)Google Scholar
  23. 23.
    Margaritis, D.: Distribution-free learning of Bayesian network structure in continuous domains. In: Proceedings of AAAI (2005)Google Scholar
  24. 24.
    Margaritis, D., Bromberg, F.: Efficient Markov network discovery using particle filter. Comput. Intell. 25(4), 367–394 (2009)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Margaritis, D., Thrun, S.: Bayesian network induction via local neighborhoods. In: Proceedings of NIPS06 (2000)Google Scholar
  26. 26.
    McCallum, A.: Efficiently inducing features of conditional random fields. In: Proceedings of Uncertainty in Artificial Intelligence (UAI) (2003)Google Scholar
  27. 27.
    Minka, T.: Divergence measures and message passing. Tech. rep. Microsoft Research (2005)Google Scholar
  28. 28.
    Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  29. 29.
    Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Voigt, H.M., Ebeling,W., Rechenberg, I., Schwefel, H.P. (eds.) Parallel Problem Solving from NaturePPSN IV. Lecture Notes in Computer Science, vol. 1141, pp. 178187. Springer, Berlin (1996). doi:10.1007/3-540-61723-X982Google Scholar
  30. 30.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)Google Scholar
  31. 31.
    Ravikumar, P., Wainwright, M.J., Lafferty, J.D.: High-dimensional Ising model selection using L1-regularized logistic regression. Ann. Stat. 38, 1287–1319 (2010). doi: 10.1214/09-AOS691 CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Santana, R.: Estimation of distribution algorithms with kikuchi approximations. Evol. Comput. 13(1), 67–97 (2005). doi: 10.1162/1063656053583496 CrossRefGoogle Scholar
  33. 33.
    Schlüter, F.: A survey on independence-based markov networks learning. Artif. Intell. Rev., 1–25 (2012). doi: 10.1007/s10462-012-9346-y
  34. 34.
    Shakya, S., McCall, J.: Optimization by estimation of distribution with deum framework based on Markov random fields. Int. J. Autom. Comput. 4(3), 262272. (2007)
  35. 35.
    Shakya, S., Santana, R., Lozano, J.A.: A markovianity based optimisation algorithm. Genet. Program Evolvable Mach. 13(2), 159–195 (2012)CrossRefGoogle Scholar
  36. 36.
    Schmidt, M., Murphy, K., Fung, G., Rosales, R.: Structure learning in random fields for heart motion abnormality detection. In: IEEE Conference on Computer Vision and Pattern Recognition, 2008, pp. 1–18. CVPR (2008). doi:
  37. 37.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search. Adaptive Computation and Machine Learning Series. MIT Press, Cambridge (2000)Google Scholar
  38. 38.
    Van Haaren, J., Davis, J.: Markov network structure learning: a randomized feature generation approach. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. (2012)
  39. 39.
    Van Haaren, J., Davis, J., Lappenschaar, M., Hommersom, A.: Exploring disease interactions using Markov networks. In: Proceedings of the AAAI-2013 (HIAI-2013). Bellevue, Washington, 15 July (2013)Google Scholar
  40. 40.
    Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1(1–2), 1–305 (2008)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Federico Schlüter
    • 1
  • Facundo Bromberg
    • 1
  • Alejandro Edera
    • 1
  1. 1.Lab. DHARMa of Artificial Intelligence, Departamento de Sistemas de información, Facultad Regional MendozaUniversidad Tecnológica NacionalMendozaArgentina

Personalised recommendations