Decomposable (probabilistic) models are log-linear models generated by acyclic hypergraphs, and a number of nice properties enjoyed by them are known. In many applications the following selection problem naturally arises: given a probability distribution p over a finite set V of n discrete variables and a positive integer k, find a decomposable model with tree-width k that best fits p. If H is the generating hypergraph of a decomposable model and pH is the estimate of p under the model, we can measure the closeness of pH to p by the information divergence D(p:pH), so that the problem above reads: given p and k, find an acyclic, connected hypergraph H of tree-width k such that D(p:pH) is minimum. It is well-known that this problem is NP-hard. However, for k=1 it was solved by Chow and Liu in a very efficient way; thus, starting from an optimal Chow-Liu solution, a few forward-selection procedures have been proposed with the aim at finding a `good' solution for an arbitrary k. We propose a backward-selection procedure which starts from the (trivial) optimal solution for k=n−1, and we show that, in a study case taken from literature, our procedure succeeds in finding an optimal solution for every k.
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A probabilistic communication structure considers the setting with communication restrictions in which each pair of players has a probability to communicate directly. In this paper, we consider a more general framework, called a probabilistic communication structure with fuzzy coalition, that allows any player to have a participation degree to cooperate within a coalition. A maximal product spanning tree, indicating a way of the greatest possibility to communicate among the players, is introduced where the unique path from one player to another is optimal. We present a feasible procedure to find the maximal product spanning trees. Furthermore, for games under this model, a new solution concept in terms of the average tree solution is proposed and axiomatized by defining a restricted game in Choquet integral form.
Migrace z pohledu Bible: jedny dějiny, jedno řešení - s přihlédnutím ke Komenského chápání Bible. Odezvy Komenského poslání a odkazu v sárospatacké "schole".