Marginalization in models generated by compositional expressions
Kybernetika, Tome 51 (2015) no. 4, pp. 541-570
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
DOI : 10.14736/kyb-2015-4-0541
Classification : 05C65, 05C85, 60E99, 65C50, 68T37
Keywords: compositional expression; compositional model; marginalization; syntax tree
@article{10_14736_kyb_2015_4_0541,
     author = {Malvestuto, Francesco M.},
     title = {Marginalization in models generated by compositional expressions},
     journal = {Kybernetika},
     pages = {541--570},
     year = {2015},
     volume = {51},
     number = {4},
     doi = {10.14736/kyb-2015-4-0541},
     mrnumber = {3423187},
     zbl = {06537773},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0541/}
}
TY  - JOUR
AU  - Malvestuto, Francesco M.
TI  - Marginalization in models generated by compositional expressions
JO  - Kybernetika
PY  - 2015
SP  - 541
EP  - 570
VL  - 51
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0541/
DO  - 10.14736/kyb-2015-4-0541
LA  - en
ID  - 10_14736_kyb_2015_4_0541
ER  - 
%0 Journal Article
%A Malvestuto, Francesco M.
%T Marginalization in models generated by compositional expressions
%J Kybernetika
%D 2015
%P 541-570
%V 51
%N 4
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0541/
%R 10.14736/kyb-2015-4-0541
%G en
%F 10_14736_kyb_2015_4_0541
Malvestuto, Francesco M. Marginalization in models generated by compositional expressions. Kybernetika, Tome 51 (2015) no. 4, pp. 541-570. doi: 10.14736/kyb-2015-4-0541

[1] Aho, A. V., Hopcroft, J. E., Ullman, J. D.: Data Structures and Algorithms. Addison-Wesley Pub. Co, Reading 1987. | MR | Zbl

[2] Aji, S. M., McEliece, R.-J.: The generalized distributive law. IEEE Trans. Inform. Theory 46 (2000), 325-343. | DOI | MR | Zbl

[3] Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. ACM 30 (1983), 479-513. | DOI | MR | Zbl

[4] Bína, V., Jiroušek, R.: Marginalization in multidimensional compositional models. Kybernetika 42 (2006), 405-422. | MR | Zbl

[5] Gaubert, S., Plus, Max: Methods and applications of (max, +) linear algebra. In: Proc. XIV Symp. on Theoretical Aspects of Computer Science Hansestatdt Luebeck 1997. | DOI

[6] Jiroušek, R.: Composition of probability measures on finite spaces. In: Proc. XIII International Conf. on Uncertainty in Artificial Intelligence (D. Geiger and P. P. Shenoy, eds.), Morgan Kaufmann, San Francisco 1997, pp. 274-281.

[7] Jiroušek, R.: Marginalization in composed probabilistic models. In: Proc. XVI International Conf. on Uncertainty in Artificial Intelligence, (C. Boutilier and M. Goldszmidt, eds.), Morgan-Kauffmann Pub., San Francisco 2000, vol. C, pp. 301-308. | DOI

[8] Jiroušek, R.: Decomposition of multidimensional distributions represented by perfect sequences. Ann. Math. Artif. Intelligence 5 (2002), 215-226. | DOI | MR | Zbl

[9] Jiroušek, R.: Foundations of compositional model theory. Int. J. General Systems 40 (2011), 623-678. | DOI | MR | Zbl

[10] Jiroušek, R.: Local computations in Dempster-Shafer theory of evidence. Int. J. Approx. Reasoning 53 (2012), 1155-1167. | DOI | MR | Zbl

[11] Jiroušek, R.: On causal compositional models: simple examples. 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. | DOI

[12] Jiroušek, R., Kratochvíl, V.: Marginalization algorithm for compositional models. In: Proc. XI International Conference on Information Processing and Management of Uncertainty in Knowledge-Bases Systems (IPMU 2006) (B. Bouchon-Meunier and R.R. Yager, eds.), pp. 2300-2307.

[13] Jiroušek, R., Kratochvíl, V.: Foundations of compositional models: structural properties. Int. J. General Systems 44 (2015), 2-25. | DOI | MR

[14] Jiroušek, R., Shenoy, P. P.: Compositional models in valuation-based systems. Int. J. Approx. Reasoning 55 (2014), 277-293. | DOI | MR | Zbl

[15] Jiroušek, R., Vejnarová, J.: General framework for multidimensional models. Int. J. General Systems 18 (2003), 107-127. | DOI | Zbl

[16] 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.

[17] Kohlas, J.: Information algebras: generic structures for inference. Springer-Verlag, 2003. | DOI | Zbl

[18] Kohlas, J., Pouly, M., Schneuwly, C.: Generic local computation. J. Comput. System Sciences 78 (2012), 348-369. | DOI | MR | Zbl

[19] Kohlas, J., Schmid, J.: An algebraic theory of information: an introduction and survey. Information 5 (2014), 219-254. | DOI

[20] Kohlas, J., Shenoy, P. P.: Computation in valuation algebras. In: Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 5: Algorithms for Uncertainty and Defeasible Reasoning (J. Kohlas and S. Moral, eds.), Kluwer, Dordrecht 2000, pp. 5-39. | DOI | MR | Zbl

[21] Kohlas, J., Wilson, N.: Semiring induced valuation algebra: exact and approximate local computation algorithms. Artificial Intelligence 172 (2008), 1360-1399. | DOI | MR

[22] Kratochvíl, V.: Probabilistic compositional models: solution of an equivalence problem. Int. J. Approx. Reasoning 54 (2013), 590-601. | DOI | MR

[23] Kschinschang, F. R., Frey, B. J., Loeliger, H.-A.: Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory 47 (2001), 498-519. | DOI | MR

[24] Lauritzen, S. L.: Graphical Models. Oxford University Press, Oxford 1996. | DOI | MR

[25] Litvinov, G. L., (eds.), S. N. Sergeev: Proc. of the International Workshop TROPICAL-07 on Tropical and Idempotent Mathematics. Contemporary Mathematics 495 (2007), American Mathematical Society. | DOI | MR

[26] Malvestuto, F. M.: A join-like operator to combine data cubes, and answer queries from multiple data cubes. ACM Trans. Database Syst. 39 (2014), 3, 1-31. | DOI | MR

[27] Malvestuto, F. M.: Equivalence of compositional expressions and independence relations in compositional models. Kybernetika 50 (2014), 322-362. | DOI | MR

[28] Malvestuto, F. M.: Erratum: Equivalence of compositional expressions and independence relations in compositional models. Kybernetika 51 (2015), 387-388. | DOI | MR

[29] Speyer, D., Sturmfels, B.: Tropical mathematics. Mathematics Magazine 82 (2009), 163-173. | DOI | MR | Zbl

Cité par Sources :