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.
|Original language||English (US)|
|Number of pages||30|
|Journal||Journal of the American Statistical Association|
|State||Published - Dec 13 2018|
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A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments
Harman, R. (Creator), Filová, L. (Creator), Richtarik, P. (Creator), Harman, R. (Creator) & Filová, L. (Creator), figshare, 2018
DOI: 10.6084/m9.figshare.7461740.v1, http://hdl.handle.net/10754/664476