Robust Regularized Discriminant Analysis Based on Implicit Weighting
Kalina, Jan; Hlinka, Jaroslav
2016 - anglický 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. Klíčová slova: high-dimensional data; classification analysis; robustness; outliers; regularization Plné texty jsou dostupné v digitálním repozitáři NUŠL 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 - anglický Klíčová slova: nonlinear equations; systems of equations; trust-region methods; quasi-Newton methods; adjoint Broyden methods; numerical algorithms; numerical experiments Plné texty jsou dostupné v digitálním repozitáři NUŠL 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 - anglický 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. Klíčová slova: neural networks; analog unit; rational weight; cut languages; computational power Plné texty jsou dostupné v digitálním repozitáři NUŠL 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 - anglický 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. Klíčová slova: differential item functioning; non-linear regression; logistic regression; item response theory Plné texty jsou dostupné v digitálním repozitáři NUŠL 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 - anglický 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 Klíčová slova: robust estimation; outliers; diagnostic tools; nonlinear regression; residuals Dokument je dostupný na externích webových stránkách. 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

Discerning Two Words by a Minimum Size Automaton
Wiedermann, Jiří
2016 - anglický Klíčová slova: finite automaton; discerning two words; complexity Plné texty jsou dostupné v digitálním repozitáři NUŠL Discerning Two Words by a Minimum Size Automaton

Wiedermann, Jiří
Ústav informatiky, 2016

Report on the Last Work by Dr. Erich Nuding
Rohn, Jiří
2016 - anglický This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for researchers working in the area of interval computations because of the intriguing concept of the "fourth modality" which has not been rediscovered during a quarter of century which has elapsed since its original formulation. Klíčová slova: set-valued mapping; interval linear equations; solution set; fourth modality Plné texty jsou dostupné v digitálním repozitáři NUŠL Report on the Last Work by Dr. Erich Nuding

This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for ...

Rohn, Jiří
Ústav informatiky, 2016

Some Robust Estimation Tools for Multivariate Models
Kalina, Jan
2015 - anglický Standard procedures of multivariate statistics and data mining for the analysis of multivariate data are known to be vulnerable to the presence of outlying and/or highly influential observations. This paper has the aim to propose and investigate specific approaches for two situations. First, we consider clustering of categorical data. While attention has been paid to sensitivity of standard statistical and data mining methods for categorical data only recently, we aim at modifying standard distance measures between clusters of such data. This allows us to propose a hierarchical agglomerative cluster analysis for two-way contingency tables with a large number of categories, based on a regularized measure of distance between two contingency tables. Such proposal improves the robustness to the presence of measurement errors for categorical data. As a second problem, we investigate the nonlinear version of the least weighted squares regression for data with a continuous response. Our aim is to propose an efficient algorithm for the least weighted squares estimator, which is formulated in a general way applicable to both linear and nonlinear regression. Our numerical study reveals the computational aspects of the algorithm and brings arguments in favor of its credibility. Klíčová slova: robust data mining; high-dimensional data; cluster analysis; outliers Dokument je dostupný na externích webových stránkách. Some Robust Estimation Tools for Multivariate Models

Standard procedures of multivariate statistics and data mining for the analysis of multivariate data are known to be vulnerable to the presence of outlying and/or highly influential observations. This ...

Kalina, Jan
Ústav informatiky, 2015

Nonlinear Conjugate Gradient Methods
Lukšan, Ladislav; Vlček, Jan
2015 - anglický Modifications of nonlinear conjugate gradient method are described and tested. Klíčová slova: minimization; nonlinear conjugate gradient methods; comparison of methods; efficiency of methods Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. Nonlinear Conjugate Gradient Methods

Modifications of nonlinear conjugate gradient method are described and tested.

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2015

A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea
Vlček, Jan; Lukšan, Ladislav
2015 - anglický A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all stored corrected difference vectors are conjugate and the quasi-Newton conditions with these vectors are satisfied. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency. Klíčová slova: large scale unconstrained optimization; numerical experiments; limited-memory variable metric method; BNS method; quasi-Newton method; convergence Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea

A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2015