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 ...

Daniel, M.; Kratochvíl, Václav
Ústav teorie informace a automatizace, 2018

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 ...

Plajner, Martin; Vomlel, Jiří
Ústav teorie informace a automatizace, 2018

Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
2018 - anglický 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. Klíčová slova: robust statistics; multivariate data; correlation coefficient; econometrics Dokument je dostupný na externích webových stránkách. 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 ...

Kalina, Jan
Ústav teorie informace a automatizace, 2018

SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE
Doskar, M.; Novák, J.; Zeman, Jan
2017 - anglický 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. Klíčová slova: Wang tiling; microstructure synthesis; microstructure-informed enrichment functions; extended finite element method Dokument je dostupný na externích webových stránkách. 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 ...

Doskar, M.; Novák, J.; Zeman, Jan
Ústav teorie informace a automatizace, 2017

Question Selection Methods for Adaptive Testing with Bayesian Networks
Plajner, Martin; Magauina, A.; Vomlel, Jiří
2017 - anglický 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. Klíčová slova: Computerized Adaptive Testing; Question Selection Methods; Bayesian Networks Dokument je dostupný na externích webových stránkách. 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 ...

Plajner, Martin; Magauina, A.; Vomlel, Jiří
Ústav teorie informace a automatizace, 2017

Analysis of truncated data with application to the operational risk estimation
Volf, Petr
2017 - anglický 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. Klíčová slova: operational risk; statistical analysis; truncated data Dokument je dostupný na externích webových stránkách. 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 ...

Volf, Petr
Ústav teorie informace a automatizace, 2017

Appearance Acquisition and Analysis of Effect Coatings
Filip, Jiří; Maile, F. J.
2017 - anglický Klíčová slova: effect coatings; appearance capturing; polychromatic; particle orientation Dokument je dostupný na externích webových stránkách. Appearance Acquisition and Analysis of Effect Coatings

Filip, Jiří; Maile, F. J.
Ústav teorie informace a automatizace, 2017

Risk-Sensitive Optimality in Markov Games
Sladký, Karel; Martínez Cortés, V. M.
2017 - anglický 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. Klíčová slova: two-person Markov games; communicating Markov chains; risk-sensitive optimality; dynamic programming Dokument je dostupný na externích webových stránkách. 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 ...

Sladký, Karel; Martínez Cortés, V. M.
Ústav teorie informace a automatizace, 2017

Multi-period Factor Model of a Loan Portfolio
Šmíd, Martin; Dufek, J.
2017 - anglický We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each on two factors: a common one, having a general distribution, and an individual one, following an AR(1) process. The default of a loan happens if the wealth stops to be su cient for repaying the loan. We show that the mapping transforming the common factors into the probability of default (PD) and the loss given default (LGD) is one-to-one twice continuously differentiable. As the transformation is not analytically tractable, we propose a numerical technique for its computation and demonstrate its accuracy by a numerical study.\nWe show that the results given by our multi-period model may differ signi cantly from\nthose resulting from single-period models, and demonstrate that our model naturally replicates\nthe empirically observed decrease of PDs within a portfolio in time. In addition, we give a formula for the overall loss of the portfolio and, as an example of its application, we formulate a simple optimal scoring decision problem and discuss its solution. Klíčová slova: Credit Risk; Structural Factor Models; Loan Portfolio Management Dokument je dostupný na externích webových stránkách. Multi-period Factor Model of a Loan Portfolio

We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each on two ...

Šmíd, Martin; Dufek, J.
Ústav teorie informace a automatizace, 2017

Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan; Peštová, B.
2017 - anglický 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. Klíčová slova: Heteroscedasticity; Regression median; Diagnostic tools; Asymptotics Dokument je dostupný na externích webových stránkách. Various Approaches to Szroeter’s Test for Regression Quantiles

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 ...

Kalina, Jan; Peštová, B.
Ústav teorie informace a automatizace, 2017