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A Note on Factorization of Belief Functions
Jiroušek, Radim ; Shenoy, P. P.
The paper compares two main types of factorization of belief functions (one based on the Dempster´s rule of combination, the other based on the operator of composition) and shows that both the approaches are equivalent to each other in case of unconditional factorization and shows what are the differences when overlapping factorization is studied.
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Conditioning and Flexibility in Compositional Models
Kratochvíl, Václav
Reasoning by cases or assumptions is a common form of human reasoning. In case of probability reasoning, this is modeled by conditioning of a multidimensional probability distribution. Compositional models are defined as a multidimensional distributions assembled from a (so called generating) sequence of lowdimensional probability distributions, with the help of operators of composition. In this case, the conditioning process can be viewed as a transformation of one generating sequence into another one. It appears that the conditioning process is simple when conditioning variable appears in the argument of the first distribution of the corresponding generating sequence. That is why we introduce the so called flexible sequences. Flexible sequences are those, which can be reordered in many ways that each variable can appears among arguments of the first distribution. In this paper, we study the problem of flexibility in light of the very recent solution of the equivalence problem.
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Motivace různých charakterizací ekvivalentních persegramů
Kratochvíl, Václav
In this paper we give the motivation and introduction for indirect characterization of equivalence. We have found three operations on persegram remaining induced independence model. By combining them together, one can generate a class of equivalent models. We are not sure whether one can generate the whole class. This problem is closely connected with the above mentioned problem of invariant properties.
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Aplikace bayesovských sítích ve hře Minesweepe
Vomlelová, M. ; Vomlel, Jiří
We use the computer game of Minesweeper to illustrate few modeling tricks utilized when applying Bayesian network (BN) models in real applications. Among others, we apply rank-one decomposition (ROD) toconditional probability tables (CPTs) representing addition. Typically, this transformation helps to reduce the computational complexity of probabilistic inference with the BN model. However, in this paper we will see that (except for the total sum node) when ROD is applied to the whole CPT it does not bring any savings for the BN model of Minesweeper. Actually, in order to gain from ROD we need minimal rank-one decompositions of CPTs when the state of the dependent variable is observed. But this is not known and it is a topic for our future research.
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Experimentální srovnání triangulačních heuristik na transformovaných sítích BN2O
Vomlel, Jiří ; Savický, Petr
In this paper we present results of experimental comparisons of several triangulation heuristics on bipartite graphs. Our motivation for testing heuristics on the family of bipartite graphs is the rank-one decomposition of BN2O networks. A BN2O network is a Bayesian network having the structure of a bipartite graph with all edges directed from the top level toward the bottom level and where all conditional probability tables are noisy-or gates. After applying the rank-one decomposition, which adds an extra level of auxiliary nodes in between the top and bottom levels, and after removing simplicial nodes of the bottom level we get so called BROD graph. This is an undirected bipartite graph. It is desirable for efficiency of the inference to find a triangulation of the BROD graph having the sum of table sizes for all cliques of the triangulated graph as small as possible. From this point of view, the minfill heuristics perform in average better than other tested heuristics (minwidth, h1, and mcs).
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