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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 ...
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 ...
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 ...
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 ...
Gradient Descent Parameter Learning of Bayesian Networks under Monotonicity Restrictions
Plajner, Martin; Vomlel, Jiří
2018 - English
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.
Keywords:
Bayesian networks; Learning model parameters; monotonicity condition
Fulltext is available at external website.
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 ...
Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
2018 - English
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
Keywords:
robust statistics; multivariate data; correlation coefficient; econometrics
Fulltext is available at external website.
Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation ...
SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE
Doskar, M.; Novák, J.; Zeman, Jan
2017 - English
Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The fluctuation fields are then used as enrichment basis in Extended Finite Element Method (XFEM) to reduce number of unknowns in problems with fully resolved microstructural geometry synthesized by means of the tiling concept. In addition, the XFEM basis functions are taken as reduced modes of a detailed discretization in order to circumvent the need for non-standard numerical quadratures. The methodology is illustrated with a scalar steady-state problem.
Keywords:
Wang tiling; microstructure synthesis; microstructure-informed enrichment functions; extended finite element method
Fulltext is available at external website.
SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE
Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The ...
Question Selection Methods for Adaptive Testing with Bayesian Networks
Plajner, Martin; Magauina, A.; Vomlel, Jiří
2017 - English
The performance of Computerized Adaptive Testing systems, which are used for testing of human knowledge, relies heavily on methods selecting correct questions for tested students. In this article we propose three different methods selecting questions with Bayesian networks as students’ models. We present the motivation to use these methods and their mathematical description. Two empirical datasets, paper tests of specific topics in mathematics and Czech language for foreigners, were collected for the purpose of methods’ testing. All three methods were tested using simulated testing procedure and results are compared for individual methods. The comparison is done also with the sequential selection of questions to provide a relation to the classical way of testing. The proposed methods are behaving much better than the sequential selection which verifies the need to use a better selection method. Individually, our methods behave differently, i.e., select different questions but the success rate of model’s predictions is very similar for all of them. This motivates further research in this topic to find an ordering between methods and to find the best method which would provide the best possible selections in computerized adaptive tests.
Keywords:
Computerized Adaptive Testing; Question Selection Methods; Bayesian Networks
Fulltext is available at external website.
Question Selection Methods for Adaptive Testing with Bayesian Networks
The performance of Computerized Adaptive Testing systems, which are used for testing of human knowledge, relies heavily on methods selecting correct questions for tested students. In this article we ...
Analysis of truncated data with application to the operational risk estimation
Volf, Petr
2017 - English
Analysis of operational risk often faces problems arising from the structure of available data, namely of left truncation and occurrence of heavy-tailed loss values. We deal with model given by lognormal dostribution contaminated by the Pareto one and to use of the Cramér-von Mises, Anderson-Darling, and Kolmogorov-Smirnov minimum distance estimators. Analysis is based on MC studies. The main objective is to propose a method of statistical analysis and modeling for the distribution of sum of\nlosses over a given period, particularly of its right quantiles.
Keywords:
operational risk; statistical analysis; truncated data
Fulltext is available at external website.
Analysis of truncated data with application to the operational risk estimation
Analysis of operational risk often faces problems arising from the structure of available data, namely of left truncation and occurrence of heavy-tailed loss values. We deal with model given by ...
Risk-Sensitive Optimality in Markov Games
Sladký, Karel; Martínez Cortés, V. M.
2017 - English
The article is devoted to risk-sensitive optimality in Markov games. Attention is focused on Markov games evolving on communicating Markov chains with two-players with opposite aims. Considering risk-sensitive optimality criteria means that total reward generated by the game is evaluated by exponential utility function with a given risk-sensitive coefficient. In particular, the first player (resp. the secondplayer) tries to maximize (resp. minimize) the long-run risk sensitive average reward. Observe that if the second player is dummy, the problem is reduced to finding optimal policy of the Markov decision chain with the risk-sensitive optimality. Recall that for the risk sensitivity coefficient equal to zero we arrive at traditional optimality criteria. In this article, connections between risk-sensitive and risk-neutral Markov decisionchains and Markov games models are studied using discrepancy functions. Explicit formulae for bounds on the risk-sensitive average long-run reward are reported. Policy iteration algorithm for finding suboptimal policies of both players is suggested. The obtained results are illustrated on numerical example.
Keywords:
two-person Markov games; communicating Markov chains; risk-sensitive optimality; dynamic programming
Fulltext is available at external website.
Risk-Sensitive Optimality in Markov Games
The article is devoted to risk-sensitive optimality in Markov games. Attention is focused on Markov games evolving on communicating Markov chains with two-players with opposite aims. Considering ...
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