Some Robust Distances for Multivariate Data
Kalina, Jan; Peštová, Barbora
2016 - English Numerous methods of multivariate statistics and data mining suffer from the presence of outlying measurements in the data. This paper presents new distance measures suitable for continuous data. First, we consider a Mahalanobis distance suitable for high-dimensional data with the number of variables (largely) exceeding the number of observations. We propose its doubly regularized version, which combines a regularization of the covariance matrix with replacing the means of multivariate data by their regularized counterparts. We formulate explicit expressions for some versions of the regularization of the means, which can be interpreted as a denoising (i.e. robust version) of standard means. Further, we propose a robust cosine similarity measure, which is based on implicit weighting of individual observations. We derive properties of the newly proposed robust cosine similarity, which includes a proof of the high robustness in terms of the breakdown point. Keywords: multivariate data; distance measures; regularization; robustness; high dimension Available on request at various institutes of the ASCR Some Robust Distances for Multivariate Data

Numerous methods of multivariate statistics and data mining suffer from the presence of outlying measurements in the data. This paper presents new distance measures suitable for continuous data. ...

Kalina, Jan; Peštová, Barbora
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

On Nominal Automata as Models of Java-like Object-Oriented Programs
Suzuki, Tomoyuki
2016 - English In this paper, we proposed a model of Java-like object-oriented programs as nominal automata and a simple method invocation checker. Available on request at various institutes of the ASCR On Nominal Automata as Models of Java-like Object-Oriented Programs

In this paper, we proposed a model of Java-like object-oriented programs as nominal automata and a simple method invocation checker.

Suzuki, Tomoyuki
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

Diagnostics for Robust Regression: Linear Versus Nonlinear Model
Kalina, Jan
2016 - English Robust statistical methods represent important tools for estimating parameters in linear as well as nonlinear econometric models. In contrary to the least squares, they do not suffer from vulnerability to the presence of outlying measurements in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. In this paper, we propose the asymptotic Goldfeld-Quandt test for the regression median. It allows to formulate a natural procedure for models with heteroscedastic disturbances, which is again based on the regression median. Further, we pay attention to nonlinear regression model. We focus on the nonlinear least weighted squares estimator, which is one of recently proposed robust estimators of parameters in a nonlinear regression. We study residuals of the estimator and use a numerical simulation to reveal that they can be severely heteroscedastic also for data generated from a model with homoscedastic disturbances. Thus, we give a warning that standard residuals of the robust nonlinear estimator may produce misleading results if used for the standard diagnostic tools Keywords: robust estimation; outliers; diagnostic tools; nonlinear regression; residuals Fulltext is available at external website. Diagnostics for Robust Regression: Linear Versus Nonlinear Model

Robust statistical methods represent important tools for estimating parameters in linear as well as nonlinear econometric models. In contrary to the least squares, they do not suffer from ...

Kalina, Jan
Ústav informatiky, 2016