Compositional models, Bayesian models and recursive factorization models

Francesco M. Malvestuto

Kybernetika (2016)

  • Volume: 52, Issue: 5, page 696-723
  • ISSN: 0023-5954

Abstract

top
Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional models generated by sequential expressions and Bayesian models. Moreover, we present a linear (graphical) algorithm for deciding if a conditional independence is valid in a given recursive factorization model.

How to cite

top

Malvestuto, Francesco M.. "Compositional models, Bayesian models and recursive factorization models." Kybernetika 52.5 (2016): 696-723. <http://eudml.org/doc/287522>.

@article{Malvestuto2016,
abstract = {Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional models generated by sequential expressions and Bayesian models. Moreover, we present a linear (graphical) algorithm for deciding if a conditional independence is valid in a given recursive factorization model.},
author = {Malvestuto, Francesco M.},
journal = {Kybernetika},
keywords = {Bayesian model; compositional model; conditional independence; Markov property; recursive model; sequential expression; Bayesian model; compositional model; conditional independence; Markov property; recursive model; sequential expression},
language = {eng},
number = {5},
pages = {696-723},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Compositional models, Bayesian models and recursive factorization models},
url = {http://eudml.org/doc/287522},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Malvestuto, Francesco M.
TI - Compositional models, Bayesian models and recursive factorization models
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 5
SP - 696
EP - 723
AB - Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional models generated by sequential expressions and Bayesian models. Moreover, we present a linear (graphical) algorithm for deciding if a conditional independence is valid in a given recursive factorization model.
LA - eng
KW - Bayesian model; compositional model; conditional independence; Markov property; recursive model; sequential expression; Bayesian model; compositional model; conditional independence; Markov property; recursive model; sequential expression
UR - http://eudml.org/doc/287522
ER -

References

top
  1. Aho, A. V., Hopcroft, J. E., Ullman, J. D., Data Structures and Algorithms., Addison-Wesley Pub. Co, Reading 1987. Zbl0487.68005MR0666695
  2. Bína, V., Jiroušek, R., 10.14736/kyb-2015-3-0525, Kybernetika 51 (2015), 525-539. Zbl1340.65011MR3391683DOI10.14736/kyb-2015-3-0525
  3. Geiger, D., Verma, T., Pearl, J., 10.1002/net.3230200504, Networks 20 (1990), 507-534. Zbl0724.05066MR1064736DOI10.1002/net.3230200504
  4. Jiroušek, R., 10.1023/a:1014591402750, In: Proc. XIII International Conference on Uncertainty in Artificial Intelligence (D. Geiger and P. P. Shenoy, eds.), Morgan Kaufmann, San Francisco 1997, pp. 274-281. DOI10.1023/a:1014591402750
  5. Jiroušek, R., 10.1023/a:1014591402750, Ann. Math. Artif. Intelligence 5 (2002), 215-226. Zbl1004.60010MR1899952DOI10.1023/a:1014591402750
  6. Jiroušek, R., 10.1080/03081079.2011.562627, Int. J. General Systems 40 (2011), 623-678. Zbl1252.68285MR2817988DOI10.1080/03081079.2011.562627
  7. Jiroušek, R., 10.1016/j.ijar.2012.06.012, Int. J. Approx. Reasoning 53 (2012), 1155-1167. Zbl1266.68177MR2971864DOI10.1016/j.ijar.2012.06.012
  8. Jiroušek, R., 10.1007/978-3-319-08795-5_53, In: Proc. XIV International Conference on Information Processing and Management of Uncertainty in Knowledge-Bases Systems (IPMU 2014) (A. Laurent et al., eds.), Part I, CCIS 442, pp. 517-526. DOI10.1007/978-3-319-08795-5_53
  9. Jiroušek, R., Kratochvíl, V., 10.1080/03081079.2014.934370, Int. J. General Systems 44 (2015), 2-25. MR3299901DOI10.1080/03081079.2014.934370
  10. Jiroušek, R., Shenoy, P. P., 10.1016/j.ijar.2013.02.002, Int. J. Approx. Reasoning 55 (2014), 277-293. Zbl1252.68310MR3133554DOI10.1016/j.ijar.2013.02.002
  11. Jiroušek, R., Vejnarová, J., 10.1002/int.10077, Int. J. Approx. Reasoning 18 (2003), 107-127. Zbl1029.68131DOI10.1002/int.10077
  12. Jiroušek, R., Vejnarová, J., Daniels, M., Composition models of belief functions., In: Proc. V Symp. on Imprecise Probabilities and Their Applications (G. De Cooman, J. Vejnarová and M. Zaffalon, eds.), Action M Agency, Prague 2007, pp. 243-252. 
  13. Kratochvíl, V., 10.1016/j.ijar.2010.12.005, Int. J. of Approx. Reasoning 52 (2011), 599-612. Zbl1214.68400MR2787020DOI10.1016/j.ijar.2010.12.005
  14. Kratochvíl, V., 10.1016/j.ijar.2013.01.002, Int. J. Approx. Reasoning 54 (2013), 590-601. MR3041095DOI10.1016/j.ijar.2013.01.002
  15. Lauritzen, S. L., Graphical Models., Oxford University Press, Oxford 1996. MR1419991
  16. Lauritzen, S. L., Dawid, A. P., Larsen, B. N., Leimer, H.-G., 10.1002/net.3230200503, Networks 20 (1990), 491-505. Zbl0743.05065MR1064735DOI10.1002/net.3230200503
  17. Maier, D., The Theory of Relational Databases., Computer Science Press, 1983. Zbl0519.68082MR0691493
  18. Malvestuto, F. M., 10.1145/2638545, ACM Trans. Database Systems 39, (2014), 3, 1-31. MR3268995DOI10.1145/2638545
  19. Malvestuto, F. M., 10.14736/kyb-2014-3-0322, Kybernetika 50 (2014), 322-362. MR3245534DOI10.14736/kyb-2014-3-0322
  20. Malvestuto, F. M., 10.14736/kyb-2015-4-0541, Kybernetika 51 (2015), 541-570. MR3423187DOI10.14736/kyb-2015-4-0541
  21. Malvestuto, F. M., A general composition operator for probabilistic compositional models., Unpublished manuscript (2016). 
  22. Pearl, J., Probabilistic Reasoning in Intelligent Systems., Morgan Kaufmann Pub., San Mateo 1988. Zbl0746.68089MR0965765
  23. Pourabbas, E., Shoshani, A., 10.1145/1206049.1206051, ACM Trans. Database Systems 32 (2007), 1, Article No. 2. DOI10.1145/1206049.1206051
  24. Tarjan, R. E., Yannakakis, M., 10.1137/0213035, SIAM J. Comput. 13 (1984), 566-579. Zbl0562.68055MR0749707DOI10.1137/0213035
  25. Verma, T., Pearl, J., Causal networks: semantics and expressiveness., In: Proc. IV Workshop on Uncertainty in Artificial Intelligence, St. Paul 1988, pp. 352-359. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.