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Information Geometry and its Applications IV
Kratochvíl, Václav
The aim of the conference is to highlight recent developments within the field of information geometry and to identify new directions of research. We are confident that we have put together an exciting program consisting of invited talks and contributed poster presentations. All titles and abstracts are included in this book. We thank Václav Kratochvíl for his terrific work with the local organisation! Special thanks go to Antje Vandenberg who managed all the administrative work in Leipzig. We are also grateful for the support that we received from Milan Studený
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Influence diagrams for speed profile optimization" computational issues
Vomlel, Jiří ; Kratochvíl, Václav
Influence diagrams were applied to diverse decision problems. However, the general theory is still not sufficiently developed if the variables are continuous or hybrid and the utility functions are nonlinear. In this paper, we study computational problems related to the application of influence diagrams to vehicle speed profile optimization and suggest an approximation of the nonlinear utility functions by piecewise linear functions.
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Proceedings of the 10th Workshop on Uncertainty Processing
Kratochvíl, Václav
WUPES 2015 is organized jointly by the Institute of Information Theory and Automation of the Czech Academy of Sciences and by the Faculty of Management, University of Economics, Prague. It is quite natural that such a meeting could not materialize if it were not for the hard work of many our colleagues and friends. This is why we want to express our gratitude to all the members of both the Programme and Organizing Committees. Last but not least, we also want to acknowledge the fact that this workshop is organized, due to the fact that the research of several members of the Organizing Committee is financially supported by grants GA CR no 15-00215S and 13-20012S.
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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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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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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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