Optimal Design of Experiments on Riemannian Manifolds
将传统欧氏空间上的最优实验设计理论推广到黎曼流形上，证明了D最优与G最优设计的等价性，并提出了一个收敛算法，数值实验显示考虑流形结构的重要性。
The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this article, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are provided. It is shown that analogously to the results in Euclidean spaces, D-optimal and G-optimal designs are equivalent on manifolds, and we provide a lower bound for the maximum prediction variance of the response evaluated over the manifold. In addition, a converging algorithm that finds the optimal experimental design on manifold data is proposed. Numerical experiments demonstrate the importance of considering the manifold structure in a designed experiment when present, and the superiority of the proposed algorithm. Supplementary materials for this article are available online.