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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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Problém ekvivalentu v kompozitních modelech
Kratochvíl, Václav
Persegram (speciální tabulka značek) zachycující strukturu kompozicionálního modelu nad množinou proměnných N indukuje množinu podmíněných nezávislostí - tzv. nezávislostní model nad N. Jak vyjádřit že dva dané persegramy indukují stejný nezávislostní model je označováno jako problém ekvivalence. V předchozích článcích byly zavedeny tři elementární operace nad persegramem zachovávající indukovaný nezávislostní model. Označujeme je jako IE-operace. Pomocí nich lze generovat celou třídu, ve výše uvedeném smyslu vekvivalentních, persegramů. Lze také odvodit tzv. nepřímou charakterizaci: Dva persegramy P,P' jsou ekvivalentí, pokud mezi P,P' existuje posloupnost persegramů taková, že pouze IE-operace byly použity aby se získa další persegram v řadě. V tomto článku najde čtenář náznak přímé charakterizace. Navzdory faktu, že finální přímá charakterizace není uvedena, je zavedeno několik invariantních vlastností ekvivalentních persegramů, které k přímé charakterizaci nejspíše povedou.
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Efektivní algoritmus na hledání redukcí v kompozicionálních modelech
Kratochvíl, Václav
Marginalizace multidimenzionálních distribucí reprezentovaných perfektními kompozicionálními modely je mnohem efektivnější než jakýkoli marginalizační proces v bayesovských sítích. Důvod je prostý. Marginalizační algoritmus, zmíněný v tomto článku, využívá informací zakódovaných ve struktuře kompozicionálních modelů, které se v bayseovských sítích musí složitě vypočítat. V tomto článku se zabýváme jednou podsekcí marginalizačního algoritmu - marginalizací redukcí. Je zde představen nový rychlejší způsob hledání redukcí v kompozicionálních modelech.
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