Number of found documents: 1578
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### 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 digital repository of the ASCR 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

### Principy statistického uvažování Kalina, Jan 2016 - Czech Available in digital repository of the ASCR Principy statistického uvažování

Kalina, Jan
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 digital repository of the ASCR New Quasi-Newton Method for Solving Systems of Nonlinear Equations

Ústav informatiky, 2016

### Discerning Two Words by a Minimum Size Automaton Wiedermann, Jiří 2016 - English Keywords: finite automaton; discerning two words; complexity Available in a digital repository NRGL 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 - English 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. Keywords: set-valued mapping; interval linear equations; solution set; fourth modality Available in a digital repository NRGL 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

### 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

### Analýza výskytu a příčin nebezpečných situací na vozovkách Bouchner, P.; Jiřina, Marcel; Novák, Mirko; Novotný, S.; Poláček, I. 2015 - Czech Available at various institutes of the ASCR Analýza výskytu a příčin nebezpečných situací na vozovkách

Bouchner, P.; Jiřina, Marcel; Novák, Mirko; Novotný, S.; Poláček, I.
Ústav informatiky, 2015

### Nonlinear Conjugate Gradient Methods Lukšan, Ladislav; Vlček, Jan 2015 - English Modifications of nonlinear conjugate gradient method are described and tested. Keywords: minimization; nonlinear conjugate gradient methods; comparison of methods; efficiency of methods Available in digital repository of the ASCR Nonlinear Conjugate Gradient Methods

Modifications of nonlinear conjugate gradient method are described and tested.

Ústav informatiky, 2015

### A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea Vlček, Jan; Lukšan, Ladislav 2015 - English 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. Keywords: large scale unconstrained optimization; numerical experiments; limited-memory variable metric method; BNS method; quasi-Newton method; convergence Available in digital repository of the ASCR 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 ...

Ústav informatiky, 2015

### Some Robust Estimation Tools for Multivariate Models Kalina, Jan 2015 - English 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. Keywords: robust data mining; high-dimensional data; cluster analysis; outliers Fulltext is available at external website. 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