Towards a Novel Probabilistic Graphical Model of Sequential Data: Fundamental Notions and a Solution to the Problem of Parameter Learning

  • Edmondo Trentin
  • Marco Bongini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7477)

Abstract

Probabilistic graphical modeling via Hybrid Random Fields (HRFs) was introduced recently, and shown to improve over Bayesian Networks (BNs) and Markov Random Fields (MRFs) in terms of computational efficiency and modeling capabilities (namely, HRFs subsume BNs and MRFs). As in traditional graphical models, HRFs express a joint distribution over a fixed collection of random variables. This paper introduces the major definitions of a proper dynamic extension of regular HRFs (including latent variables), aimed at modeling arbitrary-length sequences of sets of (time-dependent) random variables under Markov assumptions. Suitable maximum pseudo-likelihood algorithms for learning the parameters of the model from data are then developed. The resulting learning machine is expected to fit scenarios whose nature involves discovering the stochastic (in)dependencies amongst the random variables, and the corresponding variations over time.

Keywords

Probabilistic graphical model Hidden Markov model Hybrid Random Field Sequence Classification 

References

  1. 1.
    Bongini, M., Trentin, E.: Towards a Novel Probabilistic Graphical Model of Sequential Data: A Solution to the Problem of Structure Learning and an Empirical Evaluation. In: Mana, N., Schwenker, F., Trentin, E. (eds.) ANNPR 2012. LNCS (LNAI), vol. 7477, pp. 82–92. Springer, Heidelberg (2012)Google Scholar
  2. 2.
    Freno, A., Trentin, E.: Hybrid Random Fields: A Scalable Approach to Structure and Parameter Learning in Probabilistic Graphical Models. Springer (2011)Google Scholar
  3. 3.
    Freno, A., Trentin, E., Gori, M.: A Hybrid Random Field Model for Scalable Statistical Learning. Neural Networks 22, 603–613 (2009)CrossRefGoogle Scholar
  4. 4.
    Freno, A., Trentin, E., Gori, M.: Scalable Pseudo-Likelihood Estimation in Hybrid Random Fields. In: Elder, J.F., Fogelman-Souli, F., Flach, P., Zaki, M. (eds.) Proceedings of the 15th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2009), pp. 319–327. ACM (2009)Google Scholar
  5. 5.
    Freno, A., Trentin, E., Gori, M.: Scalable Statistical Learning: A Modular Bayesian/Markov Network Approach. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN 2009), pp. 890–897. IEEE (2009)Google Scholar
  6. 6.
    Ghahramani, Z.: Learning Dynamic Bayesian Networks. In: Giles, C.L., Gori, M. (eds.) IIASS-EMFCSC-School 1997. LNCS (LNAI), vol. 1387, pp. 168–197. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Kindermann, R., Laurie Snell, J.: Markov Random Fields and Their Applications. American Mathematical Society, Providence (1980)MATHCrossRefGoogle Scholar
  8. 8.
    Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In: Proc. 18th International Conf. on Machine Learning, pp. 282–289. Morgan Kaufmann, San Francisco (2001)Google Scholar
  9. 9.
    Lauritzen, S.L.: Graphical Models. Oxford University Press (1996)Google Scholar
  10. 10.
    Pearl, J.: Bayesian networks: A model of self-activated memory for evidential reasoning. In: Proceedings of the 7th Conference of the Cognitive Science Society, pp. 329–334. University of California, Irvine (1985)Google Scholar
  11. 11.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Edmondo Trentin
    • 1
  • Marco Bongini
    • 1
  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità degli Studi di SienaSienaItaly

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