Radoslav Harman

Radoslav Harman
Comenius University Bratislava · Department of Applied Mathematics and Statistics

PhD.

About

51
Publications
4,674
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466
Citations
Introduction
Radoslav Harman currently works at the Department of Applied Mathematics and Statistics, Comenius University in Bratislava. Radoslav does research in Statistics, Experimental design, Monte-Carlo methods and Optimization.

Publications

Publications (51)
Article
We describe a universal conditional distribution method for uniform sampling from n-spheres and n-balls, based on properties of a family of radially symmetric multivariate distributions. The method provides us with a unifying view on several known algorithms as well as enabling us to construct novel variants. We give a numerical comparison of the k...
Article
Full-text available
Let the design of an experiment be represented by an $s$-dimensional vector $\boldsymbol{w}$ of weights with non-negative components. Let the quality of $\boldsymbol{w}$ for the estimation of the parameters of the statistical model be measured by the criterion of $D$-optimality defined as the $m$-th root of the determinant of the information matrix...
Article
Full-text available
We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to the performan...
Article
Full-text available
In the area of statistical planning, there is a large body of theoretical knowledge and computational experience concerning so-called optimal approximate designs of experiments. However, for an approximate design to be executed in practice, it must be converted into an exact, i.e., integer, design, which is usually done via rounding procedures. Alt...
Article
Full-text available
We propose an algorithm for computing efficient approximate experimental designs that can be applied in the case of very large grid-like design spaces. Such a design space typically corresponds to the set of all combinations of multiple genuinely discrete factors or densely discretized continuous factors. The proposed algorithm alternates between t...
Article
An algorithm is provided for calculating the minimum-volume enclosing ellipsoid (MVEE) for a large dataset stored in a separate database, for which the existing algorithms run out of memory or become prohibitively slow. The focus is on tall datasets, i.e., those consisting of huge numbers of data points of moderate dimensionality. The proposed Big...
Preprint
Full-text available
For computing efficient approximate designs of multifactor experiments, we propose a simple algorithm based on adaptive exploration of the grid of all combinations of factor levels. We demonstrate that the algorithm significantly outperforms several state-of-the-art competitors for problems with discrete, continuous, as well as mixed factors. Impor...
Article
Full-text available
The problem of iterated partial summations is solved for some discrete distributions defined on finite supports. The power method, usually used as a computational approach to the problem of finding matrix eigenvalues and eigenvectors, is in some cases an effective tool to prove the existence of the limit distribution, which is then expressed as a s...
Article
D-efficient saturated subsets are natural initial solutions of various algorithms applied in statistics and computational geometry. We propose two greedy heuristics for the construction of D-efficient saturated subsets: an improvement of the method suggested by Galil and Kiefer in the context of D-optimal experimental designs and a modification of...
Article
Full-text available
Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax, and sequential appro...
Preprint
Full-text available
Let $\mathcal{F}$ be a set consisting of $n$ real vectors of dimension $m \leq n$. For any saturated, i.e., $m$-element, subset $\mathcal{S}$ of $\mathcal{F}$, let $\mathrm{vol}(\mathcal{S})$ be the volume of the parallelotope formed by the vectors of $\mathcal{S}$. A set $\mathcal{S}^*$ is called a $D$-optimal saturated subset of $\mathcal{F}$, if...
Preprint
Full-text available
We propose a method of removal of design points that cannot support any E-optimal experimental design of a linear regression model with uncorrelated observations. The proposed method can be used to reduce the size of some large E-optimal design problems such that they can be efficiently solved by semidefinite programming. This paper complements the...
Article
We propose a method for removing design points that cannot support any E-optimal experimental design of a linear regression model with uncorrelated observations. The proposed method can be used to reduce the size of some large -optimal design problems such that they can be efficiently solved by semidefinite programming. This paper complements the r...
Preprint
Full-text available
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases an effective tool to prove the existence of the limit distribution, which is then expressed as a solution of a...
Code
An R function for computing D-optimal approximate designs of experiments based on: https://arxiv.org/abs/1801.05661
Code
An R function for computing A-optimal and I-optimal approximate designs of experiments based on: https://arxiv.org/abs/1801.05661
Article
Full-text available
Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax and sequential approa...
Article
Full-text available
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show that the problem can be restated as constrained A-optimality in an artificial model. This permits using recent...
Article
Full-text available
In this paper, we study the problem of D-optimal experimental design under two linear constraints, which can be interpreted as simultaneous restrictions on the size and on the cost of the experiment. For computing a size- and cost-constrained approximate D-optimal design, we propose a specification of the “barycentric” multiplicative algorithm with...
Article
Full-text available
Suppose that we intend to perform an experiment consisting of a set of independent trials. The mean value of the response of each trial is assumed to be equal to the sum of the effect of the treatment selected for the trial, and some nuisance effects, e.g., the effect of a time trend, or blocking. In this model, we examine optimal approximate desig...
Article
Full-text available
Consider an experiment, where a new drug is tested for the first time on human subjects - healthy volunteers. Such experiments are often performed as dose-escalation studies, where a set of increasing doses is pre-selected, individuals are grouped into cohorts and a dose is given to subjects in a cohort only if the preceding dose was already given...
Article
Full-text available
Utilizing a typology for space filling into what we call “soft” and “hard” methods, we introduce the central notion of “privacy sets” for dealing with the latter. This notion provides a unifying framework for standard designs without replication, Latin hypercube designs, and Bridge designs, among many others. We introduce a heuristic algorithm base...
Conference Paper
We prove a mathematical programming characterization of approximate partial D-optimality under general linear constraints. We use this characterization with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive...
Conference Paper
We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with...
Article
Hysteresis loop measurements are frequently used to assess the magnetic quality of a nanomaterial under an external magnetic field. Based on the values of the hysteresis parameters, it is possible to decide whether the nanomaterial meets requirements of a given application. In this work, we present a new approach to the measurement of the hysteresi...
Article
Full-text available
Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of constructing an approximate D-optimal experimental design with simultaneous restrictions on the size and on the total...
Article
Consider a linear regression experiment with uncorrelated real-valued observations and a finite design space. An approximate experimental design is stratified if it allocates given proportions of trials to selected non-overlapping partitions of the design space. To calculate an approximate D-optimal stratified design, we propose two multiplicative...
Article
For computing exact designs of experiments under multiple resource constraints, we developed a heuristic method related to the Detmax procedure. To illustrate the performance of the heuristic, we computed D-efficient designs for a block model with limits on the numbers of blocks, for a quadratic regression model with simultaneous marginal and cost...
Article
Consider the quadratic regression model on the q-dimensional cube [−1, 1]q. The purpose of this article is to exhibit designs for the quadratic regression that are criterion robust in the sense of maximin efficiency within the class of all orthogonally invariant information functions. For the case of the standard quadratic regression on an interval...
Article
A new method for computing exact experimental designs for linear regression models by integer quadratic programming is proposed. The key idea is to use the criterion of DQ-optimality, which is a quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix. Several numerical examples a...
Article
Full-text available
In the paper we consider the linear regression model of the first degree on the vertices of the d-dimensional unit cube and its extension by an intercept term, which can be used, e.g., to model unbiased or biased weighing of d objects on a spring balance. In both settings, we can restrict our search for approximate optimal designs to the convex com...
Article
Full-text available
Liang and Ng (Metrika 68:83–98, 2008) proposed a componentwise conditional distribution method for L p -uniform sampling on L p -norm n-spheres. On the basis of properties of a special family of L p -norm spherical distributions we suggest a wide class of algorithms for sampling uniformly distributed points on n-spheres and n-balls in L p spaces, g...
Article
Full-text available
In the paper, we solve the problem of computing the maximin efficient design with respect to the class of all orthogonally invariant criteria. It turns out that on a finite experimental domain, the maximin efficient design can be computed by the methods of semidefinite programming. Using this approach, we can deal with the non-differentiability inh...
Article
The grape vine moth, Lobesia botrana (Denis and Schiffermuller) (Lepidoptera: Tortricidae), attacks vineyards mostly in Southern Europe and Northern Africa. The efficiency of most control methods depends on the treatment of pest populations at their most susceptible stages, therefore the prediction of the moth's development cycle would help greatly...
Article
In the paper we show that the equidistant sampling designs are optimal for the model of Brownian motion with a quadratic drift and for any of its submodels. This result holds for all Loewner isotonic criteria of parametric optimality continuous on the set of regular information matrices, as well as for the mean squared error of the best linear unbi...
Article
The present paper analyzes the linear regression model with a nonzero intercept term on the vertices of a d-dimensional unit cube. This setting may be interpreted as a model of weighing d objects on a spring balance with a constant bias. We give analytic formulas for E-optimal designs, as well as their minimal efficiencies under the class of all or...
Article
In the paper, we solve the n-point optimal prediction design problem for the simplest nontrivial finite discrete spectrum linear regression models with correlated observations. We show that for all the models in consideration, there exists an optimal prediction design supported on at most three distinct points, which can be computed using one-dimen...
Article
Full-text available
In the paper we solve the problem of D ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression...
Article
An experimental design is said to be c-optimal if it minimizes the variance of the best linear unbiased estimator of , where c is a given vector of coefficients, and [beta] is an unknown vector parameter of the model in consideration. For a linear regression model with uncorrelated observations and a finite experimental domain, the problem of appro...
Article
An experimental design is said to be Schur optimal, if it is optimal with respect to the class of all Schur isotonic criteria, which includes Kiefer's criteria of Φp-optimality, distance optimality criteria and many others. In the paper we formulate an easily verifiable necessary and sufficient condition for Schur optimality in the set of all appro...
Article
We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a D-optimum design. Let [xi] be any design on a compact space with a nonsingular information matrix, and let m+[epsilon] be the maximum...
Article
Consider the linear regression model with uncorrelated errors and an experimental design ξ. In the article, we address the problem of calculating the minimal efficiency of ξ with respect to the class [InlineMediaObject not available: see fulltext.] of orthogonally invariant information criteria, containing all Kiefer’s criteria of ϕ p -optimality,...
Chapter
Suppose that we intend to perform linear regression experiments with uncorrelated errors according to a given asymptotic design ξ. The problem which we address is the question of performance-stability of ξ under change of optimality criterion. More precisely, we describe a method of how to calculate lower bounds on the minimal possible efficiency o...
Article
We propose a network of model neurones that "reads" the information encoded as a mean spiking rate by mechanisms relevant to the organism. The streams of independent irregular spiking activity with a Poisson distribution enters the network in parallel via two inputs. The network integrates both synaptic inputs and at the same time acts as a counter...
Article
Full-text available
For linear regression models with uncorrelated errors, we describe a method of deletion of design points, which do not support any D-optimal design measure. The key idea is to construct a suitable set of matrices, which contains the information matrix corresponding to an optimal design. A combination of this method with iterative algorithms speeds...

Questions

Question (1)
Question
If yes, which algorithms or methods are efficient for most optimal design problems? Which of them have an easy-to-use free implementation?

Projects

Projects (2)
Project
Design of experiments for discriminating between non-nested regression models
Project
See https://cran.r-project.org/web/packages/OptimalDesign/index.html We will be happy to answer any question about the package.