Geodesic
A short note on Perez’s approximation by dependence structure simplification
Kybernetika, Tome 43 (2007) no. 5, pp. 649-656 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Perez’s approximations of probability distributions by dependence structure simplification were introduced in 1970s, much earlier than graphical Markov models. In this paper we will recall these Perez’s models, formalize the notion of a compatible system of elementary simplifications and show the necessary and sufficient conditions a system must fulfill to be compatible. For this we will utilize the apparatus of compositional models.
Perez’s approximations of probability distributions by dependence structure simplification were introduced in 1970s, much earlier than graphical Markov models. In this paper we will recall these Perez’s models, formalize the notion of a compatible system of elementary simplifications and show the necessary and sufficient conditions a system must fulfill to be compatible. For this we will utilize the apparatus of compositional models.
Classification : 62E17, 68T30
Keywords: approximation of probability distributions; dependence structure simplification; compatibility; compositional models 
@article{KYB_2007_43_5_a4,
     author = {Jirou\v{s}ek, Radim},
     title = {A short note on {Perez{\textquoteright}s} approximation by dependence structure simplification},
     journal = {Kybernetika},
     pages = {649--656},
     year = {2007},
     volume = {43},
     number = {5},
     mrnumber = {2376329},
     zbl = {1148.68494},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_5_a4/}
}
TY  - JOUR
AU  - Jiroušek, Radim
TI  - A short note on Perez’s approximation by dependence structure simplification
JO  - Kybernetika
PY  - 2007
SP  - 649
EP  - 656
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_2007_43_5_a4/
LA  - en
ID  - KYB_2007_43_5_a4
ER  - 
%0 Journal Article
%A Jiroušek, Radim
%T A short note on Perez’s approximation by dependence structure simplification
%J Kybernetika
%D 2007
%P 649-656
%V 43
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_2007_43_5_a4/
%G en
%F KYB_2007_43_5_a4
Jiroušek, Radim. A short note on Perez’s approximation by dependence structure simplification. Kybernetika, Tome 43 (2007) no. 5, pp. 649-656. http://geodesic.mathdoc.fr/item/KYB_2007_43_5_a4/

[1] Jiroušek R.: Composition of probability measures on finite spaces. In: Proc. 13th Conf. Uncertainty in Artificial Intelligence UAI’97 (D. Geiger and P. P. Shenoy, eds.), Morgan Kaufmann, San Francisco 1997, pp. 274–281

[2] Jiroušek R.: Marginalization in composed probabilistic models. In: Proc. 16th Conf. Uncertainty in Artificial Intelligence UAI’00 (C. Boutilier and M. Goldszmidt, eds.), Morgan Kaufmann, San Francisco 2000, pp. 301–308

[3] Perez A.: Information, $\varepsilon $-sufficiency and data reduction problems. Kybernetika 1 (1965), 297–323 | MR

[4] Perez A.: Information theory methods in reducing complex decision problems. In: Trans. 4th Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (J. Kožešník, ed.), Academia, Prague 1965, pp. 55–87 | MR

[5] Perez A.: $\varepsilon $-admissible simplification of the dependence structure of a set of random variables. Kybernetika 13 (1977), 439–449 | MR

[6] Somol P., Novovičová, J., Pudil P.: Notes on the evolution of feature selection methodology. Kybernetika 43 (2007), 713–730 | MR | Zbl