A Block Version of the BNS Limited-Memory Variable Metric Method for Unconstrained Minimization
Vlček, Jan; Lukšan, Ladislav
2016 - English Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in a digital repository NRGL A Block Version of the BNS Limited-Memory Variable Metric Method for Unconstrained Minimization

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2016

Maximum Likelihood Estimation of Diagonal Covariance Matrix
Turčičová, Marie; Mandel, Jan; Eben, Kryštof
2016 - English Keywords: maximum likelihood estimation; parametric model; Fisher information; delta method Available in a digital repository NRGL Maximum Likelihood Estimation of Diagonal Covariance Matrix

Turčičová, Marie; Mandel, Jan; Eben, Kryštof
Ústav informatiky, 2016

Cut Languages in Rational Bases
Šíma, Jiří; Savický, Petr
2016 - English We introduce a so-called cut language which contains the representations of numbers in a rational base that are less than a given threshold. The cut languages can be used to refine the analysis of neural net models between integer and rational weights. We prove a necessary and sufficient condition when a cut language is regular, which is based on the concept of a quasi-periodic power series. We show that any cut language with a rational threshold is context-sensitive while examples of non-context-free cut languages are presented. Keywords: cut language; rational base; quassi-periodic power series Available in a digital repository NRGL Cut Languages in Rational Bases

We introduce a so-called cut language which contains the representations of numbers in a rational base that are less than a given threshold. The cut languages can be used to refine the analysis of ...

Šíma, Jiří; Savický, Petr
Ústav informatiky, 2016

Interval Matrices: Regularity Yields Singularity
Rohn, Jiří
2016 - English It is proved that regularity of an interval matrix implies singularity of two related interval matrices. Keywords: interval matrix; regularity; singularity Available in a digital repository NRGL Interval Matrices: Regularity Yields Singularity

It is proved that regularity of an interval matrix implies singularity of two related interval matrices.

Rohn, Jiří
Ústav informatiky, 2016

On Exact Heteroscedasticity Testing for Robust Regression
Kalina, Jan; Peštová, Barbora
2016 - English The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity. Keywords: robust estimation; outliers; variance; diagnostic tools; heteroscedasticity Available in digital repository of the ASCR On Exact Heteroscedasticity Testing for Robust Regression

The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also ...

Kalina, Jan; Peštová, Barbora
Ústav informatiky, 2016

Robust Regularized Discriminant Analysis Based on Implicit Weighting
Kalina, Jan; Hlinka, Jaroslav
2016 - English In bioinformatics, regularized linear discriminant analysis is commonly used as a tool for supervised classification problems tailormade for high-dimensional data with the number of variables exceeding the number of observations. However, its various available versions are too vulnerable to the presence of outlying measurements in the data. In this paper, we exploit principles of robust statistics to propose new versions of regularized linear discriminant analysis suitable for highdimensional data contaminated by (more or less) severe outliers. The work exploits a regularized version of the minimum weighted covariance determinant estimator, which is one of highly robust estimators of multivariate location and scatter. The performance of the novel classification methods is illustrated on real data sets with a detailed analysis of data from brain activity research. Keywords: high-dimensional data; classification analysis; robustness; outliers; regularization Available in a digital repository NRGL Robust Regularized Discriminant Analysis Based on Implicit Weighting

In bioinformatics, regularized linear discriminant analysis is commonly used as a tool for supervised classification problems tailormade for high-dimensional data with the number of variables ...

Kalina, Jan; Hlinka, Jaroslav
Ústav informatiky, 2016

New Quasi-Newton Method for Solving Systems of Nonlinear Equations
Lukšan, Ladislav; Vlček, Jan
2016 - English Keywords: nonlinear equations; systems of equations; trust-region methods; quasi-Newton methods; adjoint Broyden methods; numerical algorithms; numerical experiments Available in a digital repository NRGL New Quasi-Newton Method for Solving Systems of Nonlinear Equations

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2016

Neural Networks Between Integer and Rational Weights
Šíma, Jiří
2016 - English The analysis of the computational power of neural networks with the weight parameters between integer and rational numbers is refined. We study an intermediate model of binary-state neural networks with integer weights, corresponding to finite automata, which is extended with an extra analog unit with rational weights, as already two additional analog units allow for Turing universality. We characterize the languages that are accepted by this model in terms of so-called cut languages which are combined in a certain way by usual string operations. We employ this characterization for proving that the languages accepted by neural networks with an analog unit are context-sensitive and we present an explicit example of such non-context-free languages. In addition, we formulate a sufficient condition when these networks accept only regular languages in terms of quasi-periodicity of parameters derived from their weights. Keywords: neural networks; analog unit; rational weight; cut languages; computational power Available in a digital repository NRGL Neural Networks Between Integer and Rational Weights

The analysis of the computational power of neural networks with the weight parameters between integer and rational numbers is refined. We study an intermediate model of binary-state neural networks ...

Šíma, Jiří
Ústav informatiky, 2016

Detection of Differential Item Functioning with Non-Linear Regression: Non-IRT Approach Accounting for Guessing
Drabinová, Adéla; Martinková, Patrícia
2016 - English In this article, we present a new method for estimation of Item Response Function and for detection of uniform and non-uniform Differential Item Functioning (DIF) in dichotomous items based on Non-Linear Regression (NLR). Proposed method extends Logistic Regression (LR) procedure by including pseudoguessing parameter. NLR technique is compared to LR procedure and Lord’s and Raju’s statistics for three-parameter Item Response Theory (IRT) models in simulation study based on Graduate Management Admission Test. NLR shows superiority in power at low rejection rate over IRT methods and outperforms LR procedure in power for case of uniform DIF detection. Our research suggests that the newly proposed non-IRT procedure is an attractive and user friendly approach to DIF detection. Keywords: differential item functioning; non-linear regression; logistic regression; item response theory Available in a digital repository NRGL Detection of Differential Item Functioning with Non-Linear Regression: Non-IRT Approach Accounting for Guessing

In this article, we present a new method for estimation of Item Response Function and for detection of uniform and non-uniform Differential Item Functioning (DIF) in dichotomous items based on ...

Drabinová, Adéla; Martinková, Patrícia
Ústav informatiky, 2016

Discerning Two Words by a Minimum Size Automaton
Wiedermann, Jiří
2016 - English Keywords: finite automaton; discerning two words; complexity Available in a digital repository NRGL Discerning Two Words by a Minimum Size Automaton

Wiedermann, Jiří
Ústav informatiky, 2016