D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations
Statistics Theory
2017-03-07 v1 Optimization and Control
Statistics Theory
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.
Cite
@article{arxiv.1703.01777,
title = {D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations},
author = {Yohann De Castro and F Gamboa and D Henrion and R Hess and J. -B Lasserre},
journal= {arXiv preprint arXiv:1703.01777},
year = {2017}
}