MAT TRIAD 2019: Book of Abstracts
Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
2019 - English This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains. Keywords: proceedings; conference; matrix analysis Available on request at various institutes of the ASCR MAT TRIAD 2019: Book of Abstracts

This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers ...

Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
Ústav informatiky, 2019

A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
Lukšan, Ladislav; Vlček, Jan
2019 - English In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Keywords: nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments Available at various institutes of the ASCR A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, ...

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2019

Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Vlček, Jan; Lukšan, Ladislav
2019 - English To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method. Keywords: unconstrained minimization; limited-memory variable metric methods; the repeated Byrd-Nocedal-Schnabel update; the Lyapunov matrix equation; the conjugate directions; global convergence; numerical results Available at various institutes of the ASCR Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods

To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2019

How to down-weight observations in robust regression: A metalearning study
Kalina, Jan; Pitra, Zbyněk
2018 - English Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is becoming popular in statistical learning and there is an increasing number of metalearning applications also in the analysis of economic data sets. Still, not much attention has been paid to its limitations and disadvantages. For this purpose, we use various linear regression estimators (including highly robust ones) over a set of 30 data sets with economic background and perform a metalearning study over them as well as over the same data sets after an artificial contamination. We focus on comparing the prediction performance of the least weighted squares estimator with various weighting schemes. A broader spectrum of classification methods is applied and a support vector machine turns out to yield the best results. While results of a leave-1-out cross validation are very different from results of autovalidation, we realize that metalearning is highly unstable and its results should be interpreted with care. We also focus on discussing all possible limitations of the metalearning methodology in general. Keywords: metalearning; robust statistics; linear regression; outliers Available on request at various institutes of the ASCR How to down-weight observations in robust regression: A metalearning study

Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is ...

Kalina, Jan; Pitra, Zbyněk
Ústav informatiky, 2018

The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases.
Šíma, Jiří
2017 - English We briefly survey the basic concepts and results concerning the computational power of neural networks which basically depends on the information content of weight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classified within the Chomsky and finer complexity hierarchies. Then we refine the analysis between integer and rational weights by investigating an intermediate model of integer-weight neural networks with an extra analog rational-weight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using so-called cut languages. Our analysis reveals an interesting link to an active research field on non-standard positional numeral systems with non-integer bases. Within this framework, we introduce a new concept of quasi-periodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy. Keywords: neural network; Chomsky hierarchy; beta-expansion; cut language Available at various institutes of the ASCR The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases.

We briefly survey the basic concepts and results concerning the computational power of neural networks which basically depends on the information content of weight parameters. In particular, recurrent ...

Šíma, Jiří
Ústav informatiky, 2017

Semigroup Structure of Sets of Solutions to Equation X^s = X^m
Porubský, Štefan
2017 - English Using an idempotent semigroup approach we describe the semigroup and group structure of the set of solutions to equation X^m = X^s in successive steps over a periodic commutative semigroup, over multiplicative semigroups of factor rings of residually finite commutative rings and finally over multiplicative semigroups of factor rings of residually finite commutative principal ideal domains. The analysis is done through the use of the maximal subsemigroups and groups corresponding to an idempotent of the corresponding semigroup and in the case of residually finite PID’s employing the available analysis of the Euler-Fermat Theorem as given in [11]. In particular the case when this set of solutions is a union of groups is handled. As a simple application we show a not yet noticed group structure of the set of solutions to x^n = x connected with the message space of RSA cryptosystems and Fermat pseudoprimes. Keywords: set of solutions; idempotent; maximal semigroup corresponding to an idempotent; maximal group corresponding to an idempotent; equation X^s = X^m; finite commutative ring with identity element; residually finite commutative principal ideal domains Available on request at various institutes of the ASCR Semigroup Structure of Sets of Solutions to Equation X^s = X^m

Using an idempotent semigroup approach we describe the semigroup and group structure of the set of solutions to equation X^m = X^s in successive steps over a periodic commutative semigroup, over ...

Porubský, Štefan
Ústav informatiky, 2017

Idempotents, Group Membership and their Applications
Porubský, Štefan
2017 - English S.Schwarz in his paper [165] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought [167] into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory. Keywords: multiplicative semigroup; finite semigroups; power semigroups; idempotent elements; finite commutative rings; principal ideal domain; Euler-Fermat theorem; Wilson theorem; matrices over fields; maximal groups contained in a semigroup; periodic sequence; multiplicative semigroup of Zm; semigroup of circulant Boolean matrices Available on request at various institutes of the ASCR Idempotents, Group Membership and their Applications

S.Schwarz in his paper [165] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought [167] into play the maximal subsemigroups and thus he embodied the ...

Porubský, Štefan
Ústav informatiky, 2017

The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases
Šíma, Jiří
2017 - English We briefly survey the basic concepts and results concerning the computational power of neural networks which basically depends on the information content of weight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classified within the Chomsky and finer complexity hierarchies. Then we refine the analysis between integer and rational weights by investigating an intermediate model of integer-weight neural networks with an extra analog rational-weight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using so-called cut languages. Our analysis reveals an interesting link to an active research field on non-standard positional numeral systems with non-integer bases. Within this framework, we introduce a new concept of quasi-periodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy. Keywords: neural network; Chomsky hierarchy; beta-expansion; cut language Available at various institutes of the ASCR The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases

We briefly survey the basic concepts and results concerning the computational power of neural networks which basically depends on the information content of weight parameters. In particular, recurrent ...

Šíma, Jiří
Ústav informatiky, 2017

Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript
Porubský, Štefan
2017 - English Keywords: STP cipher; Josef Růžek; Karol Cigáň; František Moravec; Czechoslovak military cryptography; Word War II Available on request at various institutes of the ASCR Application and Misapplication of the Czechoslovak STP Cipher During WWII - Report on an Unpublished Manuscript

Porubský, Štefan
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