On the Optimization of Initial Conditions for a Model Parameter Estimation
Matonoha, Ctirad; Papáček, Š.; Kindermann, S.
2017 - English The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on the initial condition. Numerical experiments show that the discretized optimal initial condition attains only two values. The number of jumps between these values is inversely proportional to the value of a diffusion coefficient D (characterizing the biophysical and numerical process). The smaller value of D is, the larger number of jumps occurs. Keywords: FRAP; sensitivity analysis; optimal experimental design; parameter estimation; finite differences Available in digital repository of the ASCR On the Optimization of Initial Conditions for a Model Parameter Estimation

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis ...

Matonoha, Ctirad; Papáček, Š.; Kindermann, S.
Ústav informatiky, 2017

On the optimal initial conditions for an inverse problem of model parameter estimation
Matonoha, Ctirad; Papáček, Š.
2017 - English Available in digital repository of the ASCR On the optimal initial conditions for an inverse problem of model parameter estimation

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2017

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 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

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