**866**

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**Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter**

Jiroušek, R.; Kratochvíl, Václav

2018 - English
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the Dempster-Shafer theory of evidence. Up to now, there was no direct way to get the expected value of a utility function in D-S 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.
Keywords:
*expected utility; Dempster-Shafer theory; Shenoy's operator*
Fulltext is available at external website.
Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter

Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the Dempster-Shafer theory of evidence. Up to now, there ...

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**Employing Bayesian Networks for Subjective Well-being Prediction**

Švorc, Jan; Vomlel, Jiří

2018 - English
This contribution aims at using Bayesian networks for modelling the relations between the individual subjective well-being (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.
Keywords:
*Subjective well-being; Bayesian networks*
Fulltext is available at external website.
Employing Bayesian Networks for Subjective Well-being Prediction

This contribution aims at using Bayesian networks for modelling the relations between the individual subjective well-being (SWB) and the individual material situation. The material situation is ...

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**Representations of Bayesian Networks by Low-Rank Models**

Tichavský, Petr; Vomlel, Jiří

2018 - English
Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks deﬁned as the product of these CPTs may become intractable by conventional methods of BN inference because of their dimensionality. In many cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in the so-called Kruskal form as a sum of rank-one components. Such representation would be equivalent to adding one artiﬁcial parent to all random variables and deleting all edges between the variables. The most difﬁcult task is to ﬁnd such a representation given a set of marginals or CPTs of the random variables under consideration. In the former case, it is a problem of joint canonical polyadic (CP) decomposition of a set of tensors. The latter ﬁtting problem can be solved in a similar manner. We apply a recently proposed alternating direction method of multipliers (ADMM), which assures that the model has a probabilistic interpretation, i.e., that all elements of all factor matrices are nonnegative. We perform experiments with several well-known Bayesian networks.\n\n
Keywords:
*canonical polyadic tensor decomposition; conditional probability tables; marginal probability tables*
Fulltext is available at external website.
Representations of Bayesian Networks by Low-Rank Models

Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks deﬁned as the product of these CPTs may become intractable by conventional ...

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**Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains**

Sladký, Karel

2018 - English
In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.
Keywords:
*continuous-time Markov decision chains; exponential utility functions; certainty equivalent; mean-variance optimality; connections between risk-sensitive and risk-neutral optimality*
Fulltext is available at external website.
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains

In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential ...

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**Internet věcí v praxi**

Zajíček, Milan

2018 - Czech
Předpokladem práce s mikrokontrolery je pochopení základních principů jejich komunikace s okolím a možné způsoby jejich programování. Mikrokontroler ESP8266 je jedním z nejznámějších obvodů používaných v aplikacích pro internet věcí. Jednou z vývojových platforem, která se o ESP8266 opírá, je modulární systém Wemos D1 mini, který umožňuje přímou komunikaci s PC prostřednictvím USB portu a disponuje dostatkem vstupních a výstupních periférií pro stavbu jednoduchých IoT zařízení. Pro programování je použito vývojové prostředí ArduinoIde. Tento tutorial provede úplného začátečníka od instalace software až k sestavení termostatu pro spínání silové zátěže. Prerequisite of working with microcontrollers is understanding the basic principles of their communication with the environment and possible ways of their programming. The ESP8266 microcontroller is one of the most popular chips used in Internet of things applications. Wemos D1 mini is one of development platforms behind the ESP8266,which allows direct communication with the PC via a USB port and has plenty of input and output peripherals to build simple IoT devices. The ArduinoIde development environment is used for programming. The thermostatic switch is made as a result of this tutorial.
Keywords:
*microcontrollers; Internet of things; ESP8266*
Fulltext is available at external website.
Internet věcí v praxi

Předpokladem práce s mikrokontrolery je pochopení základních principů jejich komunikace s okolím a možné způsoby jejich programování. Mikrokontroler ESP8266 je jedním z nejznámějších obvodů ...

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**Multi-Objective Optimization Problems with Random Elements - Survey of Approaches**

Kaňková, Vlasta

2018 - English
Many economic and financial situations depend simultaneously on a random element and a decision parameter. Mostly, it is possible to influence the above mentioned situation only by an optimization model depending on a probability measure. This optimization problem can be static (one-stage), dynamic with finite or infinite horizon, single-objective or multi-objective. We focus on one-stage multi-objective problems corresponding to applications those are suitable to evaluate simultaneously by a few objectives. The aim of the contribution is to give a survey of different approaches (as they are known from the literature) of the above mentioned applications. To this end we start with well-known mean-risk model and continue with other known approaches. Moreover, we try to complete every model by a suitable application. Except an analysis of a choice of the objective functions type we try to discuss suitable constraints set with respect to the problem base, possible investigation and relaxation. At the end we mention properties of the problem in the case when the theoretical „underlying“ probability measure is replaced by its „deterministic“ or „stochastic“ estimate.
Keywords:
*multi-objective optimization problems; random element; mean-risk model; deterministic approach; stochastic multi-objective problems; constraints set; relaxation*
Fulltext is available at external website.
Multi-Objective Optimization Problems with Random Elements - Survey of Approaches

Many economic and financial situations depend simultaneously on a random element and a decision parameter. Mostly, it is possible to influence the above mentioned situation only by an optimization ...

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**On attempts to characterize facet-defining inequalities of the cone of exact games**

Studený, Milan; Kroupa, Tomáš; Kratochvíl, Václav

2018 - English
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) non-redundant description of these cones by means of the so-called facet-defining 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 facet-defining inequalities for these cones. We introduce the concept of an irreducible min-balanced set system and conjecture that the facet-defining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facet-defining inequalities for this cone are those which correspond to irreducible min-balanced 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.
Keywords:
*exact game; extremity; irreducible; balanced*
Fulltext is available at external website.
On attempts to characterize facet-defining inequalities of the cone of exact games

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) non-redundant ...

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**Solution of Emission Management Problem**

Šmíd, Martin; Kozmík, Václav

2018 - English
Optimal covering of emissions stemming from random production is a multistage stochastic programming problem. Solving it in a usual way - by means of deterministic equivalent - is possible only given an unrealistic approximation of random parameters. There exists an efficient way of solving multistage problems - stochastic dual dynamic programming (SDDP), however, it requires the inter-stage independence of random parameters, which is not the case which our problem. In the paper, we discuss a modified version of SDDP, allowing for some form of interstage dependence.
Keywords:
*Multi-stage stochastic programming; Emission management; SDDP; time dependence*
Fulltext is available at external website.
Solution of Emission Management Problem

Optimal covering of emissions stemming from random production is a multistage stochastic programming problem. Solving it in a usual way - by means of deterministic equivalent - is possible only given ...

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**How to down-weight observations in robust regression: A metalearning study**

Kalina, Jan; Pitra, Z.

2018 - English
Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is becoming popular in statistical learning and there is an increasing number of metalearning applications also in the analysis of economic data sets. Still, not much attention has been paid to its limitations and disadvantages. For this purpose, we use various linear regression estimators (including highly robust ones) over a set of 30 data sets with economic background and perform a metalearning study over them as well as over the same data sets after an artificial contamination.
Keywords:
*metalearning; robust statistics; linear regression; outliers*
Fulltext is available at external website.
How to down-weight observations in robust regression: A metalearning study

Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is ...

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**About Two Consonant Conflicts of Belief Functions**

Daniel, M.; Kratochvíl, Václav

2018 - English
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 non-conflicting parts, as well as with W. Liu’s degree of conflict.
Keywords:
*belief function; conflict; consonant*
Fulltext is available at external website.
About Two Consonant Conflicts of Belief Functions

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 ...

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