Přehled metod strojového učení
Kalina, Jan
2016 - Czech Available on request at various institutes of the ASCR Přehled metod strojového učení

Kalina, Jan
Ústav informatiky, 2016

Principy statistického uvažování
Kalina, Jan
2016 - Czech Available on request at various institutes of the ASCR Principy statistického uvažování

Kalina, Jan
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

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

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.

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 - 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 ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2015

On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data
Papáček, Š.; Jablonský, J.; Matonoha, Ctirad
2015 - English FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model parameter estimation and then we focus on how the different methods of data pre- processing influence the confidence interval of the estimated parameters, namely the diffusion constant $p$. Finally, we present a preliminary study of two methods for the computation of a least-squares estimate $\hat{p}$ and its confidence interval. Keywords: parameter estimation; fluorescence recovery after photobleaching; diffusion equation; Moullineaux method; Fisher information matrix; sensitivity analysis; confidence intervals; uncertainty quantification Available in digital repository of the ASCR On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data

FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living ...

Papáček, Š.; Jablonský, J.; Matonoha, Ctirad
Ústav informatiky, 2015

Indecisive Belief Functions
Daniel, Milan
2015 - English This study presents an idea of indecisive functions, their general and also special definitions, plausibility and pignistic indecisive belief functions. The rich structure of indecisive belief functions is studied in general, and also in special views: both general substructures and indecisive belief functions on three-element and general finite frames of discernment. We are focused to pignistic and contour (plausibility) indecisive belief functions, including their mutual relationship in our study. The later have interesting algebraic structure related to Dempster’s rule of combination. Keywords: belief function; theory of evidence; Dempster-Shafer theory; Dempster’s semigroup Fulltext is available at external website. Indecisive Belief Functions

This study presents an idea of indecisive functions, their general and also special definitions, plausibility and pignistic indecisive belief functions. The rich structure of indecisive belief ...

Daniel, Milan
Ústav informatiky, 2015

Synergy between the Parameter Estimation and a Design Variable Optimization for FRAP Experiments
Matonoha, Ctirad; Papáček, Š.
2015 - English Available in digital repository of the ASCR Synergy between the Parameter Estimation and a Design Variable Optimization for FRAP Experiments

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2015

Dynamic Contact Problems in Bone Neoplasm Analyses and the Primal-Dual Active Set (PDAS) Method
Nedoma, Jiří
2015 - English In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful methods and efficient algorithms for their solutions. Because the geometry of the system of loaded and possible fractured bones with enlarged neoplasms changes in time, the corresponding mathematical models of tumor’s and cyst’s evolutions lead to the coupled free boundary problems and the dynamic contact problems with or without friction. The discussed parts of these models will be based on the theory of dynamic contact problems without or with Tresca or Coulomb frictions in the visco-elastic rheology. The numerical solution of the problem with Coulomb friction is based on the semi-implicit scheme in time and the finite element method in space, where the Coulomb law of friction at every time level will be approximated by its value from the previous time level. The algorithm for the corresponding model of friction will be based on the discrete mortar formulation of the saddle point problem and the primal-dual active set algorithm. The algorithm for the Coulomb friction model will be based on the fixpoint algorithm, that will be an extension of the PDAS algorithm for the Tresca friction. In this algorithm the friction bound is iteratively modified using the normal component of the Lagrange multiplier. Thus the friction bound and the active and inactive sets are updated in every step of the iterative algorithm and at every time step corresponding to the semi-implicit scheme. Keywords: dynamic contact problems; mathematical models of neoplasms - tumors and cysts; Coulomb and Tresca frictions; variational formulation; semi-implicit scheme; FEM; mortar approximation; PDAS algorithm Fulltext is available at external website. Dynamic Contact Problems in Bone Neoplasm Analyses and the Primal-Dual Active Set (PDAS) Method

In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful ...

Nedoma, Jiří
Ústav informatiky, 2015