Probabilistic Expert Systems
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Uncertain Information Processing in Expert Systems
Uncertain Information Processing in Expert Systems
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Composition of probability measures on finite spaces
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
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Composition of low-dimensional distributions, whose foundations were laid in the paper published in the Proceedings of UAI'97 (Jiroušek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In contrast to Graphical Markov Models, which define multidimensional distributions in a declarative way, this approach is rather procedural. Ordering of low-dimensional distributions into a proper sequence fully defines the respective computational procedure; therefore, a study of different types of generating sequences is one of the central problems in this field. Thus, it appears that an important role is played by special sequences that are called perfect. Their main characterization theorems are presented in this paper. However, the main result of this paper is a solution to the problem of marginalization for general sequences. The main theorem describes a way to obtain a generating sequence that defines the model corresponding to the marginal of the distribution defined by an arbitrary generating sequence. From this theorem the reader can see to what extent these computations are local; i.e., the sequence consists of marginal distributions whose computation must be made by summing up over the values of the variable eliminated (the paper deals with a finite model).