arXiv subjects

Lenka Filová

Publications and source records attributed to Lenka Filová.

7 recordsLinked to original sources

arXiv2026

Optimal allocation of trials to sub-regions in crop variety testing with multiple years and correlated genotype effects

Plant breeding and variety trials are usually conducted in multiple environments sampled from a defined target population of environments in order to characterize the performance of breeding lines or varieties. When the population is large and heterogeneous, it may be sub-divided into sub-regions or zones according to administrative and agro-ecological criteria. Analysis then focuses on prediction of performance in the individual sub-regions. Modelling the genotype effect in each sub-region as random, information can be borrowed across sub-regions using best linear unbiased prediction based on a suitable variance-covariance matrix for the genotype-zone effects. Here, we consider the important case where kinship of pedigree information is available for the genotypes under test. This information can be integrated into the variance-covariance matrix for genotype-zone effects. The objective we pursue here is to determine the optimal allocation of a fixed budget of trials to sub-regions. This design problem is solved using a combination of theory and explicit equations on one hand and numerical optimization on the other hand. Our proposed novel approach allows obtaining the optimal allocation when the number of genotypes is in the hundreds, a common setting in large plant breeding programs as well as in variety testing for economically important crops.

stat.AP↗

arXiv2025

Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints

We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artificial optimal design problem that can be solved using any existing mathematical programming technique for univariate-response optimal designs under pure linear constraints. The solution to this artificial problem can then be directly converted into an optimal design for the primary multivariate-response setting with combined linear and sparsity constraints. We demonstrate the utility and flexibility of the approach through dose-response experiments with constraints on safety, efficacy, and cost, where cost also depends on the number of distinct doses used.

stat.ME↗

arXiv2024

The Polytope of Optimal Approximate Designs: Extending the Selection of Informative Experiments

Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution. Often, however, there exists a rich set of optimal designs, and the knowledge of this set can lead to substantially greater freedom to select an appropriate experiment. In this paper, we demonstrate that the set of all optimal approximate designs generally corresponds to a polytope. Particularly important elements of the polytope are its vertices, which we call vertex optimal designs. We prove that the vertex optimal designs possess unique properties, such as small supports, and outline strategies for how they can facilitate the construction of suitable experiments. Moreover, we show that for a variety of situations it is possible to construct the vertex optimal designs with the assistance of a computer, by employing error-free rational-arithmetic calculations. In such cases the vertex optimal designs are exact, often closely related to known combinatorial designs. Using this approach, we were able to determine the polytope of optimal designs for some of the most common multifactor regression models, thereby extending the choice of informative experiments for a large variety of applications.

stat.CO↗

arXiv2021

Optimal Design of Multifactor Experiments via Grid Exploration

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. Importantly, we provide a free R code that permits direct verification of the numerical results and allows the researchers to easily compute optimal or nearly-optimal experimental designs for their own statistical models.

stat.CO↗

arXiv2019

Ascent with Quadratic Assistance for the Construction of Exact Experimental Designs

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. Although rapid, rounding procedures have many drawbacks; in particular, they often yield worse exact designs than heuristics that do not require approximate designs at all. In this paper, we build on an alternative principle of utilizing optimal approximate designs for the computation of optimal, or nearly-optimal, exact designs. The principle, which we call ascent with quadratic assistance (AQuA), is an integer programming method based on the quadratic approximation of the design criterion in the neighborhood of the optimal approximate information matrix. To this end, we present quadratic approximations of all Kiefer's criteria with an integer parameter, including D- and A-optimality and, by a model transformation, I-optimality. Importantly, we prove a low-rank property of the associated quadratic forms, which enables us to apply AQuA to large design spaces, for example via mixed integer conic quadratic solvers. We numerically demonstrate the robustness and superior performance of the proposed method for models under various types of constraints. More precisely, we compute optimal size-constrained exact designs for the model of spring-balance weighing, and optimal symmetric marginally restricted exact designs for the Scheffe mixture model. We also show how can iterative application of AQuA be used for a stratified information-based subsampling of large datasets under a lower bound on the quality and an upper bound on the cost of the subsample.

stat.CO↗

arXiv2018

A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

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 performance of state-of-the-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality that also has applications beyond experimental design, such as the construction of the minimum volume ellipsoid containing a given set of data-points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality. These formulas enable one to use REX for computing A-optimal and I-optimal designs.

stat.CO↗

arXiv2014

Heuristic construction of exact experimental designs under multiple resource constraints

The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any combination of resource constraints, we propose a tabu search heuristic that uses some ideas of the Detmax procedure. To illustrate the scope and performance of our heuristic, we computed D-efficient designs for 1) a block model with limits on the numbers of blocks and on the availability of experimental material; 2) a quadratic regression model with simultaneous marginal and cost constraints; 3) a non-linear regression model with simultaneous direct and cost constraints. As we show, the proposed heuristic generates comparable or better results than algorithms specialized for computing optimal designs under less general constraints.

stat.CO↗