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A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

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  • Radoslav Harman
  • Lenka Filová
  • Peter Richtárik

Abstract

We propose a class of subspace ascent methods for computing optimal approximate designs that covers existing algorithms as well as new and more efficient ones. 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 that 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, which 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, which enable one to use REX and some other algorithms for computing A-optimal and I-optimal designs. Supplementary materials for this article are available online.

Suggested Citation

  • Radoslav Harman & Lenka Filová & Peter Richtárik, 2020. "A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 348-361, January.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:348-361
    DOI: 10.1080/01621459.2018.1546588
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    Cited by:

    1. Sebastià Bargues, Àngela & Polo Sanz, José-Luis & García-Camacha Gutiérrez, Irene & Martín Martín, Raúl, 2023. "Practical implementation of optimal experimental design using the fractional-order Fricke–Morse bioimpedance model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Fontana, Roberto & Rapallo, Fabio & Wynn, Henry P., 2022. "Circuits for robust designs," LSE Research Online Documents on Economics 113631, London School of Economics and Political Science, LSE Library.
    3. Jacopo Paglia & Jo Eidsvik & Juha Karvanen, 2022. "Efficient spatial designs using Hausdorff distances and Bayesian optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1060-1084, September.
    4. Haoyu Wang & Chongqi Zhang, 2022. "The mixture design threshold accepting algorithm for generating $$\varvec{D}$$ D -optimal designs of the mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 345-371, April.
    5. Roberto Fontana & Fabio Rapallo & Henry P. Wynn, 2022. "Circuits for robust designs," Statistical Papers, Springer, vol. 63(5), pages 1537-1560, October.
    6. Àngela Sebastià Bargues & José-Luis Polo Sanz & Raúl Martín Martín, 2022. "Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    7. Lianyan Fu & Faming Ma & Zhuoxi Yu & Zhichuan Zhu, 2023. "Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    8. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    9. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Oliveira, Nuno M.C., 2024. "Using hierarchical information-theoretic criteria to optimize subsampling of extensive datasets," LSE Research Online Documents on Economics 121641, London School of Economics and Political Science, LSE Library.

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