D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS

Yohann de Castro (1) , F Gamboa (2) , Didier Henrion (3, 4) , Roxana Hess (3) , Jean-Bernard Lasserre (3, 2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
4 CTU - Czech Technical University in Prague

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.

Mots clés: experimental design; semidefinite programming

Domaines: Statistiques [math.ST]; Optimisation et contrôle [math.OC]

Yohann de Castro, F Gamboa, Didier Henrion, Roxana Hess, Jean-Bernard Lasserre. D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS. 2017. ⟨hal-01483490v1⟩