Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
2019 - English This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Keywords: second order elliptic PDEs; preconditioning by the inverse Laplacian; eigenvalues of the discretized preconditioned problem; nodal values of the coefficient function; Hall’s theorem; convergence of the conjugate gradient method Available in digital repository of the ASCR Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
Ústav informatiky, 2019

A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.
Kalina, Jan; Tobišková, Nicole; Tichavský, Jan
2019 - English While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be still lacking. In general, a reliable robust estimator of regression parameters should be consistent and at the same time should have a relatively small variability, i.e. the variances of individual regression parameters should be small. The aim of this paper is to compare the variability of S-estimators, MM-estimators, least trimmed squares, and least weighted squares estimators. While they all are consistent under general assumptions, the asymptotic covariance matrix of the least weighted squares remains infeasible, because the only available formula for its computation depends on the unknown random errors. Thus, we take resort to a nonparametric bootstrap comparison of variability of different robust regression estimators. It turns out that the best results are obtained either with MM-estimators, or with the least weighted squares with suitable weights. The latter estimator is especially recommendable for small sample sizes. Keywords: robustness; linear regression; outliers; bootstrap; least weighted squares Fulltext is available at external website. A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.

While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be ...

Kalina, Jan; Tobišková, Nicole; Tichavský, Jan
Ústav informatiky, 2019

Implicitly weighted robust estimation of quantiles in linear regression
Kalina, Jan; Vidnerová, Petra
2019 - English Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number of econometric applications. Although regression quantiles are commonly known as robust tools, they are vulnerable to the presence of leverage points in the data. We propose here a novel approach for the linear regression based on a specific version of the least weighted squares estimator, together with an additional estimator based only on observations between two different novel quantiles. The new methods are conceptually simple and comprehensible. Without the ambition to derive theoretical properties of the novel methods, numerical computations reveal them to perform comparably to standard regression quantiles, if the data are not contaminated by outliers. Moreover, the new methods seem much more robust on a simulated dataset with severe leverage points. Keywords: regression quantiles; robust regression; outliers; leverage points Fulltext is available at external website. Implicitly weighted robust estimation of quantiles in linear regression

Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number ...

Kalina, Jan; Vidnerová, Petra
Ústav informatiky, 2019

A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan; Neoral, A.
2019 - English Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is potentially beneficial for the analysis of economic data, we must be aware of its instability and sensitivity to outlying measurements (outliers) as well as measurement errors. The aim of this paper is to robustify the metalearning process. First, we prepare some useful theoretical tools exploiting the idea of implicit weighting, inspired by the least weighted squares estimator. These include a robust coefficient of determination, a robust version of mean square error, and a simple rule for outlier detection in linear regression. We perform a metalearning study for recommending the best linear regression estimator for a new dataset (not included in the training database). The prediction of the optimal estimator is learned over a set of 20 real datasets with economic motivation, while the least squares are compared with several (highly) robust estimators. We investigate the effect of variable selection on the metalearning results. If the training as well as validation data are considered after a proper robust variable selection, the metalearning performance is improved remarkably, especially if a robust prediction error is used. Keywords: model choice; computational statistics; robustness; variable selection Available in digital repository of the ASCR A Robustified Metalearning Procedure for Regression Estimators

Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is ...

Kalina, Jan; Neoral, A.
Ústav informatiky, 2019

On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - English This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Keywords: parameter identification; bleaching pattern; initial boundary value problem; sensitivity measure Available in digital repository of the ASCR On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2019

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; econometrics; correlation coefficient; multivariate data 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 ...

Kalina, Jan
Ústav informatiky, 2018

Datová sada pro detekci dezinformačního obsahu – případová studie Novičok v Česku
Řimnáč, Martin
2018 - Czech Publikování dezinformací na webu hraje stále větší roli, proto vyvstává otázka, jak takovému obsahu čelit, a nebo na jeho potenciální závadnost alespoň upozornit. Propaganda využívá dezinformací k relativizaci skutečností, jejichž popis se snaží většinou nepřímo zpochybnit. Příspěvek formou případové studie v konkrétní kauze formálně popisuje výroky prezentované v článcích publikovaných na webu a to včetně účelu jejich publikování, všímá si některých zajímavých aspektů prezentovaných dezinformací a hledá model pro jejich popis. Cílem příspěvku je informovat o vznikající datové sadě a ilustrovat základní použité dezinformační techniky včetně důsledků jejich použití. The paper presents a case study of the propaganda usage on a real cause of double agent Sergei Skripal. The formal model describing statements published in web articles is announced and particular interesting aspects of used disinformation are provided together with the reasons, why the disinformation is published. The paper is aimed at the presentation of the data collection to have been created and provides a brief discussion on the used propaganda techniques. Keywords: Dezinformace; Web; Entropie; Pravděpodobnost Fulltext is available at external website. Datová sada pro detekci dezinformačního obsahu – případová studie Novičok v Česku

Publikování dezinformací na webu hraje stále větší roli, proto vyvstává otázka, jak takovému obsahu čelit, a nebo na jeho potenciální závadnost alespoň upozornit. Propaganda využívá dezinformací k ...

Řimnáč, Martin
Ústav informatiky, 2018

Robust Metalearning: Comparing Robust Regression Using A Robust Prediction Error
Peštová, Barbora; Kalina, Jan
2018 - English The aim of this paper is to construct a classification rule for predicting the best regression estimator for a new data set based on a database of 20 training data sets. Various estimators considered here include some popular methods of robust statistics. The methodology used for constructing the classification rule can be described as metalearning. Nevertheless, standard approaches of metalearning should be robustified if working with data sets contaminated by outlying measurements (outliers). Therefore, our contribution can be also described as robustification of the metalearning process by using a robust prediction error. In addition to performing the metalearning study by means of both standard and robust approaches, we search for a detailed interpretation in two particular situations. The results of detailed investigation show that the knowledge obtained by a metalearning approach standing on standard principles is prone to great variability and instability, which makes it hard to believe that the results are not just a consequence of a mere chance. Such aspect of metalearning seems not to have been previously analyzed in literature. Keywords: metalearning; robust regression; outliers; robust prediction error Fulltext is available at external website. Robust Metalearning: Comparing Robust Regression Using A Robust Prediction Error

The aim of this paper is to construct a classification rule for predicting the best regression estimator for a new data set based on a database of 20 training data sets. Various estimators considered ...

Peštová, Barbora; Kalina, Jan
Ústav informatiky, 2018

An adaptive recursive multilevel approximate inverse preconditioning: Computation of the Schur complement
Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
2017 - English Available in digital repository of the ASCR An adaptive recursive multilevel approximate inverse preconditioning: Computation of the Schur complement

Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
Ústav informatiky, 2017

Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan; Peštová, Barbora
2017 - 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. Theoretical results may be simply extended to the context of multivariate quantiles Keywords: heteroscedasticity; robust statistics; regression; diagnostic tools; economic data Fulltext is available at external website. Exact Inference In Robust Econometrics under Heteroscedasticity

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, 2017