Dual optimal design and the Christoffel-Darboux polynomial

Yohann de Castro, Fabrice Gamboa, Didier Henrion, Jean-Bernard Lasserre

Abstract: The purpose of this short note is to show that the Christoffel–Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. Geometric interpretations and algorithmic consequences are mentioned.