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Problém ekvivalentu v kompozitních modelech
Kratochvíl, Václav
Structure of each Compositional model can be visualized by a tool called persegram. Every persegram over a finite non-empty set of variables N induces an independence model over N, which is a list of conditional independence statements over N. The Equivalence problem is how to characterize (in graphical terms) whether all independence statements in the model induced by persegram P are in the model induced by a second persegram P' and vice versa. Three different operations preserving independence model were introduced in previous papers. If combined, one is able to generate the (whole) class of equivalent persegrams. This characterization is indirect: Two persegrams P,P' are equivalent if there exists a sequence of persegrams from P,P' such that only so called IE-operations are performed to get next persegram in the sequence. In this paper we give the motivation and introduction for direct characterization of equivalence.
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O jednom přibližném řešení marginálního problému
Janžura, Martin
With the aid of the Maximum Entropy principle, a solution to the marginal problem is obtained in a form of parametric exponential (Gibbs-Markov) distribution. The unknown parameters can be calculated by an optimization procedure that agrees with the maximum likelihood estimate but it is numerically hardly feasible for highly dimensional systems. A numerically easily feasible solution can be obtained by the algebraic Möbius formula. The formula, unfortunately, involves terms that are not directly available but can be approximated. And the main aim of the present paper consists in this approximation.
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Doplňování fragmentů posibilistických distribucí s hodnotami v úplném svazu podle principu maximální hodnoty entropie
Kramosil, Ivan
Investigated are Boolean-valued possibilistic distributions taking their values in the power-set of all sets of positive integers. However, some of these possibility degrees may be known only fragmentally in the sense that for the characteristic sequence (identifier) of the set-value in question not all members of this sequence are known. A simple possibilistic entropy function is defined and completions of fragments of possibility degrees with respect to the classical (optimistic or global, in a sense) principle of maximal entropy as well as with respect to some weakened (local or pessimistic, in a sense) versions of this principle are introduced and analyzed.
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Podmiňovací pravidla pro klasické domněnkové funkce
Daniel, Milan
The classic belief conditioning rules (BCRs) and DSm BCRs applied to classic belief functions are briefly recalled in the contribution. A general idea of belief conditioning by a given evidence is analysed and a new plain BCR is presented. This rule is compared with both the classic and the DSm BCRs. Finally, general formulas for described BCRs and a new general BCR are presented and defined.
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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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