2017/05/24 by Zelda Mariet, Suvrit Sra, Mariet, Zelda +1
Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimal Experimental Design Methods #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1705.09677
openalex publication_date 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.