Dual optimal design and the Christoffel-Darboux polynomial

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.

Automated summary

This short note discusses the application of the Christoffel-Darboux polynomial in approximation theory and data science, as well as its role in the semi-algebraic D-optimal experimental design problem in statistics. The article uses elementary notions of convex analysis and mentions geometric interpretations and algorithmic consequences.