APPROXIMATE OPTIMAL DESIGNS FOR MULTIVARIATE POLYNOMIAL REGRESSION
成果类型：
Article
署名作者：
De Castro, Yohann; Gamboa, Fabrice; Henrion, Didier; Hesst, Roxana; Lasserre, Jean-Bernard
署名单位：
Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/18-AOS1683
发表日期：
2019
页码：
127-155
关键词：
摘要：
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semialgebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This article shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy increases. Furthermore, we provide a dual certificate ensuring finite convergence of the hierarchy and showing that the approximate optimal design can be computed numerically with our method. As a byproduct, we revisit the equivalence theorem of the experimental design theory: it is linked to the Christoffel polynomial and it characterizes finite convergence of the moment-sum-of-square hierarchies.