Approximate Optimal Designs for Multivariate Polynomial Regression

Yohann de Castro; Fabrice Gamboa; Didier Henrion; Roxana Hess; J.-B Lasserre

Approximate Optimal Designs for Multivariate Polynomial Regression

Yohann de Castro ^{1, 2} Fabrice Gamboa ³ Didier Henrion ^{4, 5} Roxana Hess ⁴ J.-B Lasserre ⁴

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

Inria de Paris, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

3 IMT - Institut de Mathématiques de Toulouse UMR5219

4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]

5 CTU - Czech Technical University in Prague

Abstract : We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) 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.

Keywords : Equivalence Theorem Linear Model Experimental design Semidefinite programming Christoffel Polynomial

Document type :

Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

Mathematics [math] / Optimization and Control [math.OC]

Complete list of metadatas

Cited literature [24 references] Display Hide Download

https://hal.laas.fr/hal-01483490
Contributor : Didier Henrion <>
Submitted on : Tuesday, October 17, 2017 - 10:41:26 AM
Last modification on : Friday, June 14, 2019 - 6:31:17 PM
Long-term archiving on : Thursday, January 18, 2018 - 12:42:10 PM

AoSv2 (2).pdf

Files produced by the author(s)

Approximate Optimal Designs for Multivariate Polynomial Regression

File

Identifiers

Collections

Citation

Export

Metrics

388

130

Contact

Approximate Optimal Designs for Multivariate Polynomial Regression

File

Identifiers

Collections

Citation

Export

Share

Metrics

388

130

Contact