Second-Order Belief Hidden Markov Models

  • Jungyeul Park
  • Mouna Chebbah
  • Siwar Jendoubi
  • Arnaud Martin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8764)


Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model.


Belief functions Dempster-Shafer theory first-order belief HMM second-order belief HMM probabilistic HMM 


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  1. 1.
    Aregui, A., Denœux, T.: Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities. International Journal of Approximate Reasoning 49(3), 575–594 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Boudaren, M.E.Y., Monfrini, E., Pieczynski, W., Aïssani, A.: Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context. EURASIP Journal on Advances in Signal Processing 134, 1–13 (2012)Google Scholar
  3. 3.
    Brants, T.: TnT – A Statistical Part-of-Speech Tagger. In: Proceedings of the Sixth Conference on Applied Natural Language Processing, pp. 224–231. Association for Computational Linguistics, Seattle (2000), Scholar
  4. 4.
    Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4(3), 244–264 (1988), Scholar
  5. 5.
    Fayad, F., Cherfaoui, V.: Object-Level Fusion and Confidence Management in a Multi-Sensor Pedestrian Tracking System. Lecture Notes in Electrical Engineering 35, 15–31 (2009)CrossRefGoogle Scholar
  6. 6.
    Fouque, L., Appriou, A., Pieczynski, W.: An evidential Markovian model for data fusion and unsupervised image classification. In: Proceedings of the Third International Conference on Information Fusion, FUSION 2000, Paris, France, July 10-13, vol. 1, pp. 25–32 (2000)Google Scholar
  7. 7.
    Huang, X.D., Ariki, Y., Jack, M.A.: Hidden Markov Models for Speech Recognition. Edinburgh University Press (1990)Google Scholar
  8. 8.
    Jendoubi, S., Yaghlane, B.B., Martin, A.: Belief Hidden Markov Model for Speech Recognition. In: Proceedings of the International Conference on Modeling, Simulation and Applied Optimization (ICMSAO 2013), Hammamet, Tunisia, April 28-30 (2013)Google Scholar
  9. 9.
    Johnson, M.: Why Doesn’t EM Find Good HMM POS-Taggers? In: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), pp. 296–305 (2007),
  10. 10.
    Jurafsky, D., Martin, J.H.: Speech and Language Processing, 2nd edn. Prentice Hall (2008)Google Scholar
  11. 11.
    Kupiec, J.: Robust part-of-speech tagging using a hidden Markov model. Computer Speech and Language 6(3), 225–242 (1992)CrossRefGoogle Scholar
  12. 12.
    Lanchantin, P., Pieczynski, W.: Unsupervised restoration of hidden nonstationary Markov chain using evidential priors. IEEE Transactions on Signal Processing - Part II 53(8), 3091–3098 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lee, L.M., Lee, J.C.: A Study on High-Order Hidden Markov Models and Applications to Speech Recognition. In: Ali, M., Dapoigny, R. (eds.) IEA/AIE 2006. LNCS (LNAI), vol. 4031, pp. 682–690. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Pieczynski, W.: Multisensor triplet Markov chains and theory of evidence. International Journal of Approximate Reasoning 45(1), 1–16 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Rabiner, L.R.: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE 77(2), 257–286 (1989)CrossRefGoogle Scholar
  16. 16.
    Ramasso, E.: Reconnaissance de séquences d’états par le Modèle des Croyances Transférables. Application à l’analyse de vidéos d’athlétisme. Ph.D. thesis, Universit Joseph-Fourier - Grenoble I (2007)Google Scholar
  17. 17.
    Ramasso, E.: Contribution of belief functions to hidden Markov models with an application to fault diagnosis. In: Proceedings of 2011 IEEE Conference on Prognostics and Health Management (PHM), Grenoble, France, September 1-4, pp. 1–6 (2011)Google Scholar
  18. 18.
    Ramasso, E., Denœux, T.: Making Use of Partial Knowledge About Hidden States in HMMs: An Approach Based on Belief Functions. IEEE Transactions on Fuzzy Systems 22(2), 395–405 (2014)CrossRefGoogle Scholar
  19. 19.
    Ramasso, E., Denœux, T., Zerhouni, N.: Partially-Hidden Markov Models. In: Proceedings of the 2nd International Conference on Belief Functions, Compiègne, France, May 9-11 (2012)Google Scholar
  20. 20.
    Serir, L., Ramasso, E., Zerhouni, N.: Time-Sliced Temporal Evidential Networks: The case of Evidential HMM with application to dynamical system analysis. In: Proceedings of 2011 IEEE Conference on Prognostics and Health Management (PHM), Montreal, Canada, June 20-23, pp. 1–10 (2011)Google Scholar
  21. 21.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
  22. 22.
    Smets, P.: Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9(1), 1–35 (1993), Scholar
  23. 23.
    Smets, P.: Analyzing the combination of conflicting belief functions. Information Fusion 8(4), 387–412 (2007), Scholar
  24. 24.
    Smets, P., Kennes, R.: The Transferable Belief Model. Artificial Intelligence 66, 191–234 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Soubaras, H.: On Evidential Markov Chains. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, J.-L., Yager, R.R. (eds.) Foundations of Reasoning under Uncertainty. STUDFUZZ, vol. 249, pp. 247–264. Springer, Heidelberg (2010), Scholar
  26. 26.
    Sudano, J.J.: Inverse Pignistic Probability Transforms. In: Proceedings of the Fifth International Conference on Information Fusion, Annapolis, MD, USA, July 8-11, vol. 2, pp. 763–768 (2002)Google Scholar
  27. 27.
    Thede, S.M., Harper, M.P.: A Second-Order Hidden Markov Model for Part-of-Speech Tagging. In: Proceedings of the 37th Annual Meeting of the Association for Computational Linguistics, pp. 175–182. Association for Computational Linguistics, College Park (1999), Scholar
  28. 28.
    Yager, R.R.: On the Dempster-Shafer Framework and New Combination rules. Information Sciences 41(2), 93–137 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Zhou, G., Su, J.: Named Entity Recognition using an HMM-based Chunk Tagger. In: Proceedings of 40th Annual Meeting of the Association for Computational Linguistics, pp. 473–480. Association for Computational Linguistics, Philadelphia (2002), Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jungyeul Park
    • 1
  • Mouna Chebbah
    • 1
    • 2
  • Siwar Jendoubi
    • 1
    • 2
  • Arnaud Martin
    • 1
  1. 1.UMR 6074 IRISAUniversité de Rennes1LannionFrance
  2. 2.LARODEC LaboratoryUniversity of Tunis,ISG TunisTunisia

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