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

Yohann de Castro(yohann.decastro***at***math.u-psud.fr)
Fabrice Gamboa(fabrice.gamboa***at***math.univ-toulouse.fr)
Didier Henrion(henrion***at***laas.fr)
Roxana Hess(roxana.hess***at***laas.fr)
Jean Bernard Lasserre(lasserre***at***laas.fr)

Abstract: 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.

Keywords: semidefinite programming; statistics; experimental design

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering (Statistics )

Citation:

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Entry Submitted: 03/13/2017
Entry Accepted: 03/13/2017
Entry Last Modified: 03/13/2017

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