Dual optimal design and the Christoffel–Darboux polynomial

Yohann De Castro; Fabrice Gamboa; Didier Henrion; Jean Bernard Lasserre

doi:10.1007/s11590-020-01680-2

Dual optimal design and the Christoffel–Darboux polynomial

Yohann De Castro
, Fabrice Gamboa
, Didier Henrion
, Jean Bernard Lasserre

Institut Camille Jordan
Université de Toulouse
Université Paul Sabatier
Faculty of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3-8
Number of pages	6
Journal	Optimization Letters
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s11590-020-01680-2
Publication status	Published - 1 Feb 2021
Externally published	Yes

Keywords

Convex analysis
Data science
Semidefinite programming
Statistics

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10.1007/s11590-020-01680-2

Cite this

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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.",

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AU - Gamboa, Fabrice

AU - Henrion, Didier

AU - Lasserre, Jean Bernard

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AB - 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.

KW - Convex analysis

KW - Data science

KW - Semidefinite programming

KW - Statistics

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Dual optimal design and the Christoffel–Darboux polynomial

Abstract

Keywords

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