The Complexity of Plate Probabilistic Models

  • Fabio G. CozmanEmail author
  • Denis D. Mauá
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9310)


Plate-based probabilistic models combine a few relational constructs with Bayesian networks, so as to allow one to specify large and repetitive probabilistic networks in a compact and intuitive manner. In this paper we investigate the combined, data and domain complexity of plate models, showing that they range from polynomial to \(\#\mathsf {P}\)-complete to \(\#\mathsf {EXP}\)-complete.


Plate Model Relational Bayesian Networks Counting Turing Machine Nested Plates Combined Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The first author was partially supported by CNPq and the second author was partially supported by FAPESP.


  1. 1.
    Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet allocation. J. Mach. Learn. Res. 3(3), 993–1022 (2003)zbMATHGoogle Scholar
  2. 2.
    Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Cambridge University Press, Cambridge (1997)zbMATHCrossRefGoogle Scholar
  3. 3.
    Buntine, W.L.: Operations for learning with graphical models. J. Artif. Intell. Res. 2, 159–225 (1994)Google Scholar
  4. 4.
    Cozman, F.G., Mauá, D.D.: Bayesian networks specified using propositional and relational constructs: combined, data, and domain complexity. In: AAAI Conference on Artificial Intelligence, pp. 3519–3525 (2015)Google Scholar
  5. 5.
    Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)zbMATHCrossRefGoogle Scholar
  6. 6.
    de Campos, C.P., Stamoulis, G., Weyland, D.: A structured view on weighted counting with relations to quantum computation and applications. Technical report 133, Electronic Colloquium on Computational Complexity (2013)Google Scholar
  7. 7.
    Gilks, W., Thomas, A., Spiegelhalter, D.: A language and program for complex Bayesian modelling. The Stat. 43, 169–178 (1993)Google Scholar
  8. 8.
    Jaeger, M.: Relational Bayesian networks. In: Conference on Uncertainty in Artificial Intelligence, pp. 266–273 (1997)Google Scholar
  9. 9.
    Jaeger, M., van den Broeck, G.: Upper and lower bounds. In: Statistical Relational AI Workshop, Liftability of Probabilistic Inference (2012)Google Scholar
  10. 10.
    Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)Google Scholar
  11. 11.
    Lunn, D., Jackson, C., Best, N., Thomas, A., Spiegelhalter, D.: The BUGS Book: A Practical Introduction to Bayesian Analysis. CRC Press/Chapman and Hall, Boca Raton (2012)Google Scholar
  12. 12.
    Lunn, D., Spiegelhalter, D., Thomas, A., Best, N.: The BUGS project: evolution, critique and future directions. Stat. Med. 28, 3049–3067 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Papadimitriou, C.H.: A note on succinct representations of graphs. Inf. Control 71, 181–185 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley Publishing, Reading (1994)Google Scholar
  15. 15.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)Google Scholar
  16. 16.
    Poole, D.: First-order probabilistic inference. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 985–991 (2003)Google Scholar
  17. 17.
    Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1–2), 107–136 (2006)CrossRefGoogle Scholar
  18. 18.
    Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82(1–2), 273–302 (1996)CrossRefGoogle Scholar
  19. 19.
    Sontag, D., Roy, D.: Complexity of inference in Latent Dirichlet Allocation. Adv. Neural Inf. Process. Syst. 24, 1008–1016 (2011)Google Scholar
  20. 20.
    Tobies, S.: The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. J. Artif. Intell. Res. 12, 199–217 (2000)zbMATHMathSciNetGoogle Scholar
  21. 21.
    Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM J. Comput. 8(3), 410–421 (1979)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Universidade de São PauloSão PauloBrazil

Personalised recommendations