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Composition of low-dimensional distribu tions, whose foundations were laid in the pa per published in the Proceedings of UAI'97 (Jirousek 1997), appeared to be an alterna tive apparatus to describe multidimensional probabilistic models. In contrast to Graphi cal Markov Models, which define multidimen sional distributions in a declarative way, this approach is rather procedural. Ordering of low-dimensional distributions into a proper sequence fully defines the respective compu tational procedure; therefore, a study of dif ferent types of generating sequences is one of the central problems in this field. Thus, it ap pears that an important role is played by spe cial 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 distri bution defined by an arbitrary generating se quence. From this theorem the reader can see to what extent these computations are lo cal; i.e., the sequence consists of marginal dis tributions whose computation must be made by summing up over the values of the vari able eliminated (the paper deals with a finite model) .
Marginalization in Composed Probabilistic Models