Quasi-uniform designs with optimal and near-optimal uniformity constant
Statistics Theory
2021-12-21 v1 Machine Learning
Machine Learning
Statistics Theory
Abstract
A design is a collection of distinct points in a given set , which is assumed to be a compact subset of , 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.
Keywords
Cite
@article{arxiv.2112.10401,
title = {Quasi-uniform designs with optimal and near-optimal uniformity constant},
author = {Luc Pronzato and Anatoly Zhigljavsky},
journal= {arXiv preprint arXiv:2112.10401},
year = {2021}
}