Geodesic
A short note on Perez’s approximation by dependence structure simplification
Kybernetika, Tome 43 (2007) no. 5, pp. 649-656

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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 
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     author = {Jirou\v{s}ek, Radim},
     title = {A short note on {Perez{\textquoteright}s} approximation by dependence structure simplification},
     journal = {Kybernetika},
     pages = {649--656},
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     mrnumber = {2376329},
     zbl = {1148.68494},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_5_a4/}
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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/