Marginalization in Composed Probabilistic Models
  Composition of low-dimensional distributions, whose foundations were laid in
the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to
be an alternative apparatus to describe multidimensional probabilistic models.
In contrast to Graphical Markov Models, which define multidomensinoal
distributions in a declarative way, this approach is rather procedural.
Ordering of low-dimensional distributions into a proper sequence fully defines
the resepctive computational procedure; therefore, a stury of different type of
generating sequences is one fo 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 presetned in this paper.
However, the main result of this paper is a solution to the problem of
margnialization 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 genearting sequence. From
this theorem the reader can see to what extent these comutations 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 finite model).
