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Causality and Intervention in Business Process Management
Bína, V. ; Jiroušek, Radim
The paper presents an algebraic approach to the modeling of causality in systems of stochastic variables. The methodology is based on an operator of a composition that provides the possibility of composing a multidimensional distribution from low-dimensional building blocks taking advantage of the dependence structure of the problem variables. The authors formally define and demonstrate on a hypothetical example a surprisingly elegant unifying approach to conditioning by a single variable and the evaluation of the effect of an intervention. Both operations are realized by the composition with a degenerated distribution and differ only in the sequence in which the operator of the composition is performed.
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An attempt to implement Compositional Models in Dempster-Shafer theory of Evidence
Kratochvíl, Václav
It has been published recently that some of the ideas for representation of multidimensional distributions in probability theory can be transferred into Dempster-Shafer theory of Evidence. Namely, they showed that multidimensional basic assignments can be rather efficiently represented in a form of so-called compositional models. These models are based on the iterative application of the operator of composition, whose definition for basic assignments has been introduced in [5]. It appears that a software tool supporting computations within compositional model is necessary for additional theoretical research in this framework. In this paper we will familiarize the reader with our first attempts and basic problems of the implementation itself.
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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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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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Efektivní algoritmus na hledání redukcí v kompozicionálních modelech
Kratochvíl, Václav
This paper deals with the problem of marginalization of multidimensional probability distributions represented by a compositional model. By the perfect one in this case. From the computational point of view this solution is more efficient than any known marginalization process for Bayesian models. This is because the process mentioned in the paper in a form of an algorithm and takes an advantage of the fact that the perfect sequence models have some information encoded; if can be obtained from the Bayesian networks by an application of rather computationally expensive procedures. One part of that algorithm is marginalization by means of reduction. This paper describe a new faster algorithm to find a reduction in a compositional model.
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