20180730 11:02 
On attempts to characterize facetdefining inequalities of the cone of exact games
Studený, Milan ; Kroupa, Tomáš ; Kratochvíl, Václav
The sets of balanced, totally balanced, exact and supermodular games play an important role in cooperative game theory. These sets of games are known to be polyhedral cones. The (unique) nonredundant description of these cones by means of the socalled facetdefining inequalities is known in cases of balanced games and supermodular games, respectively. The facet description of the cones of exact games and totally balanced games are not known and we present conjectures about what are the facetdefining inequalities for these cones. We introduce the concept of an irreducible minbalanced set system and conjecture that the facetdefining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facetdefining inequalities for this cone are those which correspond to irreducible minbalanced systems on strict subsets of the set of players and their conjugate inequalities. A consequence of the validity of the conjectures would be a novel result saying that a game m is exact if and only if m and its reflection are totally balanced.
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20180730 11:02 
Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter
Jiroušek, R. ; Kratochvíl, Václav
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the DempsterShafer theory of evidence. Up to now, there was no direct way to get the expected value of a utility function in DS theory. If eeded, one had to find a probability mass function corresponding to the considered belief function, and then  using this probability mass function  to compute the classical probabilistic expectation. In this paper, we take four different approaches to defining probabilistic representatives of a belief function and compare which one yields to the best approximations of Shenoy’s expected values of various utility functions. The achieved results support our conjecture that there does not exist a probabilistic representative of a belief function that would yield the same expectations as the Shenoy’s new operator.
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20180730 11:02 
About Two Consonant Conflicts of Belief Functions
Daniel, M. ; Kratochvíl, Václav
General belief functions usually bear some internal conflict which comes mainly from disjoint focal elements. Analogously, there is often some conflict between two (or more) belief functions. After the recent observation of hidden conflicts (seminar CJS’17 [17]), appearing at belief functions with disjoint focal elements, importance of interest in conflict of belief functions has increased. This theoretical contribution introduces a new approach to conflicts (of belief functions). Conflicts are considered independently of any combination rule and of any distance measure. Consonant conflicts are based on consonant approximations of belief functions in general; two special cases of the consonant approach based on consonant inverse pignistic and consonant inverse plausibility transforms are discussed. Basic properties of the newly defined conflicts are presented, analyzed and briefly compared with our original approaches to conflict (combinational conflict, plausibility conflict and comparative conflict), with the recent conflict based on nonconflicting parts, as well as with W. Liu’s degree of conflict.
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20180730 11:02 
Proceedings of the 11th Workshop on Uncertainty Processing
Kratochvíl, Václav ; Vejnarová, Jiřina
The Workshop on Uncertainty Processing, better known under its abbreviation WUPES, celebrates its 30year anniversary this year. In 1988, when the first Workshop took place, Czechoslovakia was still a communist country and a part of the Soviet bloc. Since then, many things have changed. For example, Czechoslovakia no longer exists as a country (because in 1993 it was peacefully split into two independent countries  Czechia and Slovakia). From this perspective, it is hard to believe that we have several participants who have attended most workshops in the the thirtyyear history of WUPES. As of now, the Program Committee has accepted, based on the extended abstracts, 21 papers to be presented at the Workshop, and 19 out of them are to be published in the present Conference Proceedings. These papers cover diverse topics, such as information processing, decision making, and data analysis; but what is common to most of them is that they are related to uncertainty calculus  Bayesian Networks, DempsterShafer Theory, Belief Functions, Probabilistic Logic, Game Theory, etc.
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20180619 19:26 
Gradient Descent Parameter Learning of Bayesian Networks under Monotonicity Restrictions
Plajner, Martin ; Vomlel, Jiří
Learning parameters of a probabilistic model is a necessary step in most machine learning modeling tasks. When the model is complex and data volume is small the learning process may fail to provide good results. In this paper we present a method to improve learning results for small data sets by using additional information about the modelled system. This additional information is represented by monotonicity conditions which are restrictions on parameters of the model. Monotonicity simplifies the learning process and also these conditions are often required by the user of the system to hold. \n\nIn this paper we present a generalization of the previously used algorithm for parameter learning of Bayesian Networks under monotonicity conditions. This generalization allows both parents and children in the network to have multiple states. The algorithm is described in detail as well as monotonicity conditions are.\n\nThe presented algorithm is tested on two different data sets. Models are trained on differently sized data subsamples with the proposed method and the general EM algorithm. Learned models are then compared by their ability to fit data. We present empirical results showing the benefit of monotonicity conditions. The difference is especially significant when working with small data samples. The proposed method outperforms the EM algorithm for small sets and provides comparable results for larger sets.
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20180619 19:26 
Employing Bayesian Networks for Subjective Wellbeing Prediction
Švorc, Jan ; Vomlel, Jiří
This contribution aims at using Bayesian networks for modelling the relations between the individual subjective wellbeing (SWB) and the individual material situation. The material situation is approximated by subjective measures (perceived economic strain, subjective evaluation of the income relative to most people in the country and to own past) and objective measures (household’s income, material deprivation, financial problems and housing defects). The suggested Bayesian network represents the relations among SWB and the variables approximating the material situation. The structure is established based on the expertise gained from literature, whereas the parameters are learnt based on empirical data from 3rd edition of European Quality of Life Study for the Czech Republic, Hungary, Poland and Slovakia conducted in 2011. Prediction accuracy of SWB is tested and compared with two benchmark models whose structures are learnt using Gobnilp software and a greedy algorithm built in Hugin software. SWB prediction accuracy of the expert model is 66,83%, which is significantly different from no information rate of 55,16%. It is slightly lower than the two machine learnt benchmark models.
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20180619 19:26 
Dynamic Bayesian Networks for the Classification of Sleep Stages
Vomlel, Jiří ; Kratochvíl, Václav
Human sleep is traditionally classified into five (or six) stages. The manual classification is time consuming since it requires knowledge of an extensive set of rules from manuals and experienced experts. Therefore automatic classification methods appear useful for this task. In this paper we extend the approach based on Hidden Markov Models by relating certain features not only to the current time slice but also to the previous one. Dynamic Bayesian Networks that results from this generalization are thus capable of modeling features related to state transitions. Experiments on real data revealed that in this way we are able to increase the prediction accuracy.
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20180619 19:26 
Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan ; Peštová, B.
Regression quantiles represent an important tool for regression analysis popular in econometric applications, for example for the task of detecting heteroscedasticity in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. The paper is devoted to heteroscedasticity testing for regression quantiles, while their most important special case is commonly denoted as the regression median. Szroeter’s test, which is one of available heteroscedasticity tests for the least squares, is modified here for the regression median in three different ways: (1) asymptotic test based on the asymptotic representation for regression quantiles, (2) permutation test based on residuals, and (3) exact approximate test, which has a permutation character and represents an approximation to an exact test. All three approaches can be computed in a straightforward way and their principles can be extended also to other heteroscedasticity tests. The theoretical results are expected to be extended to other regression quantiles and mainly to multivariate quantiles.
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20180528 15:54 
Platební regulační mechanismus jako zdroj zvyšování platů ve zdravotnictví
Grim, Jiří
Princip zdravotního pojištění předpokládá, že se pacient v případě potřeby obrátí na lékaře, který mu poskytne odbornou pomoc, přičemž výkon lékaře, výdaje za léky a doplňující vyšetření proplácí zdravotní pojišťovna. Výsledkem je spontánní nárůst nákladů zdravotní péče u nás dobře známý z devadesátých let. Je zřejmé, že v systému, ve kterém o poskytnuté zdravotní péči musí rozhodovat lékaři v kontaktu s pacienty a její náklady následně hradí zdravotní pojišťovny, chybí záporná zpětná vazba, která by působila proti růstu nákladů. Důsledkem této hrubé systémové chyby je trvalý tlak na zvyšování výdajů za poskytnutou zdravotní péči a hrozící platební neschopnost nutí zdravotní pojišťovny zavádět regulační opatření k omezení růstu nákladů.
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20180307 15:28 
Alternative Formulation of Payasclear Auction in Electricity Markets
Aussel, D. ; Červinka, Michal ; Henrion, R. ; Pištěk, Miroslav
In widely used formulation of payasclear electricity market the clearing price is given by the Lagrange multiplier of the demand sat isfaction constraint in the problem of the Independent System Operator (ISO). Following this idea, one may usually calculate the market clearing\nprice analytically even for problems of higher dimensions. However, the economic interpretation of such a market setting is in question, since the minimized criterion does not correspond neither to the cost of production nor to the overall payment of consumers. This observation motivated us\nto propose an alternative clearing mechanism where the total payment of consumers is explicitly minimized. We show existence and uniqueness of the clearing price in such a setting.
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