A Generalized Limited-Memory BNS Method Based on the Block BFGS Update
Vlček, Jan; Lukšan, Ladislav
2017 - English A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in some sense for quadratic objective functions, but it does not guarantee that the direction vectors are descent for general functions. To overcome this difficulty and utilize the advantageous properties of the block BFGS update, a block version of the limited-memory BNS method for large scale unconstrained optimization is proposed. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency. Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in digital repository of the ASCR A Generalized Limited-Memory BNS Method Based on the Block BFGS Update

A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2017

The IINC System under the ROOT Environment
Jiřina, Marcel
2017 - English Keywords: IINC; data separation; classification; multivariate data; distance; metric Available in digital repository of the ASCR The IINC System under the ROOT Environment

Jiřina, Marcel
Ústav informatiky, 2017

The use of sequential quadratic programming for solving reachability problems
Kuřátko, Jan
2017 - English Available in digital repository of the ASCR The use of sequential quadratic programming for solving reachability problems

Kuřátko, Jan
Ústav informatiky, 2017

Robust Regression Estimators: A Comparison of Prediction Performance
Kalina, Jan; Peštová, Barbora
2017 - English Regression represents an important methodology for solving numerous tasks of applied econometrics. This paper is devoted to robust estimators of parameters of a linear regression model, which are preferable whenever the data contain or are believed to contain outlying measurements (outliers). While various robust regression estimators are nowadays available in standard statistical packages, the question remains how to choose the most suitable regression method for a particular data set. This paper aims at comparing various regression methods on various data sets. First, the prediction performance of common robust regression estimators are compared on a set of 24 real data sets from public repositories. Further, the results are used as input for a metalearning study over 9 selected features of individual data sets. On the whole, the least trimmed squares turns out to be superior to the least squares or M-estimators in the majority of the data sets, while the process of metalearning does not succeed in a reliable prediction of the most suitable estimator for a given data set. Keywords: robust estimation; linear regression; prediction; outliers; metalearning Available at various institutes of the ASCR Robust Regression Estimators: A Comparison of Prediction Performance

Regression represents an important methodology for solving numerous tasks of applied econometrics. This paper is devoted to robust estimators of parameters of a linear regression model, which are ...

Kalina, Jan; Peštová, Barbora
Ústav informatiky, 2017

Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan; Peštová, Barbora
2017 - English 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. Keywords: Heteroscedasticity; Regression median; Diagnostic tools; Asymptotics Available on request at various institutes of the ASCR 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, Barbora
Ústav informatiky, 2017

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization
Vlček, Jan; Lukšan, Ladislav
2017 - English Keywords: unconstrained minimization; block variable metric methods; limited-memory methods; the BFGS update; global convergence; numerical results Available in a digital repository NRGL Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2017

Nondeterministic Computations for Which Space is More Powerful than Time
Wiedermann, Jiří
2016 - English Keywords: nondeterministic computation; crossing sequences; complexity Available in a digital repository NRGL Nondeterministic Computations for Which Space is More Powerful than Time

Wiedermann, Jiří
Ústav informatiky, 2016

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

Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem
Fabián, Zdeněk
2016 - English Keywords: score function; transformation-based score; generalized moment method; new descriptive characteristic of the data Available on request at various institutes of the ASCR Real-valued Score Function, New Description of Continuous Random Variables and the Central Limit Theorem

Fabián, Zdeněk
Ústav informatiky, 2016