Elementary Symmetric Polynomials for Optimal Experimental Design
Abstract
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture "partial volumes" and offer a graded interpolation between the widely used A-optimal design and D-optimal design models, obtaining each of them as special cases. We analyze properties of our models, and derive both greedy and convex-relaxation algorithms for computing the associated designs. Our analysis establishes approximation guarantees on these algorithms, while our empirical results substantiate our claims and demonstrate a curious phenomenon concerning our greedy method. Finally, as a byproduct, we obtain new results on the theory of elementary symmetric polynomials that may be of independent interest.
Cite
@article{arxiv.1705.09677,
title = {Elementary Symmetric Polynomials for Optimal Experimental Design},
author = {Zelda Mariet and Suvrit Sra},
journal= {arXiv preprint arXiv:1705.09677},
year = {2017}
}