A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

• 成果类型: Article
• 署名作者: Harman, Radoslav; Filova, Lenka; Richtarik, Peter
• 署名单位: Comenius University Bratislava; Johannes Kepler University Linz; King Abdullah University of Science & Technology; University of Edinburgh; Moscow Institute of Physics & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1546588
• 发表日期: 2020
• 页码: 348-361
• 关键词: linear constraints; descent; CONSTRUCTION; optimization; CONVERGENCE; support

摘要

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. for this article are available online.