Quasi-uniform designs with optimal and near-optimal uniformity constant

2021/12/20 by Luc Pronzato, Pronzato, Luc, Anatoly Zhigljavsky +1 · 3 citations
Decision Sciences · Engineering · Mathematics · #05B30 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Optimal Experimental Design Methods #Primary 65D17 #Statistics Theory (math.ST) #graph theory and CDMA systems #secondary 65D15

paper · pdf · doi:10.48550/arxiv.2112.10401

openalex publication_date 2021/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A design is a collection of distinct points in a given set X, which is assumed to be a compact subset of R^d, and the mesh-ratio of a design is the ratio of its fill distance to its separation radius. The uniformity constant of a sequence of nested designs is the smallest upper bound for the mesh-ratios of the designs. We derive a lower bound on this uniformity constant and show that a simple greedy construction achieves this lower bound. We then extend this scheme to allow more flexibility in the design construction.

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• Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutions
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• Exact ℓ^∞-separation radius of Sobol' sequences in dimension 2

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• Uniform Design: Theory and Application
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