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Employing Bayesian Networks for Subjective Well-being Prediction
Švorc, Jan; Vomlel, Jiří
2018 - anglický
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.
Klíčová slova:
Subjective well-being; Bayesian networks
Dokument je dostupný na externích webových stránkách.
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 ...
Representations of Bayesian Networks by Low-Rank Models
Tichavský, Petr; Vomlel, Jiří
2018 - anglický
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
Klíčová slova:
canonical polyadic tensor decomposition; conditional probability tables; marginal probability tables
Dokument je dostupný na externích webových stránkách.
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 ...
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains
Sladký, Karel
2018 - anglický
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.
Klíčová slova:
continuous-time Markov decision chains; exponential utility functions; certainty equivalent; mean-variance optimality; connections between risk-sensitive and risk-neutral optimality
Dokument je dostupný na externích webových stránkách.
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 ...
Proceedings of the 11th Workshop on Uncertainty Processing
Kratochvíl, Václav; Vejnarová, Jiřina
2018 - anglický
The Workshop on Uncertainty Processing, better known under its abbreviation WUPES, celebrates its 30-year 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 thirty-year 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, Dempster-Shafer Theory, Belief Functions, Probabilistic Logic, Game Theory, etc.
Klíčová slova:
uncertainty processing; artificial intelligence; bayesian networks
Dokument je dostupný na externích webových stránkách.
Proceedings of the 11th Workshop on Uncertainty Processing
The Workshop on Uncertainty Processing, better known under its abbreviation WUPES, celebrates its 30-year anniversary this year. In 1988, when the first Workshop took place, Czechoslovakia was still a ...
Multi-Objective Optimization Problems with Random Elements - Survey of Approaches
Kaňková, Vlasta
2018 - anglický
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.
Klíčová slova:
multi-objective optimization problems; random element; mean-risk model; deterministic approach; stochastic multi-objective problems; constraints set; relaxation
Dokument je dostupný na externích webových stránkách.
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 ...
On attempts to characterize facet-defining inequalities of the cone of exact games
Studený, Milan; Kroupa, Tomáš; Kratochvíl, Václav
2018 - anglický
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.
Klíčová slova:
exact game; extremity; irreducible; balanced
Dokument je dostupný na externích webových stránkách.
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 ...
Solution of Emission Management Problem
Šmíd, Martin; Kozmík, Václav
2018 - anglický
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.
Klíčová slova:
Multi-stage stochastic programming; Emission management; SDDP; time dependence
Dokument je dostupný na externích webových stránkách.
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 ...
How to down-weight observations in robust regression: A metalearning study
Kalina, Jan; Pitra, Z.
2018 - anglický
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.
Klíčová slova:
metalearning; robust statistics; linear regression; outliers
Dokument je dostupný na externích webových stránkách.
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 ...
About Two Consonant Conflicts of Belief Functions
Daniel, M.; Kratochvíl, Václav
2018 - anglický
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.
Klíčová slova:
belief function; conflict; consonant
Dokument je dostupný na externích webových stránkách.
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 ...
Gradient Descent Parameter Learning of Bayesian Networks under Monotonicity Restrictions
Plajner, Martin; Vomlel, Jiří
2018 - anglický
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.
Klíčová slova:
Bayesian networks; Learning model parameters; monotonicity condition
Dokument je dostupný na externích webových stránkách.
Gradient Descent Parameter Learning of Bayesian Networks under Monotonicity Restrictions
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 ...
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