论文标题
分层采样的分区
Partitions for stratified sampling
论文作者
论文摘要
经典的抖动采样分区$ [0,1]^d $ in $ m^d $ cubes，用于正整数$ m $，并随机将每个点放置在其中，提供了一组尺寸$ n = m^d $的点，并具有较小的差异。本说明的目的是提供适用于任意$ n $的分区的构造，并改善直率的构造。我们展示了如何构建$ d $维单元立方体的e象分区，该单位立方体具有与立方体主要对角线正交相对的超支。我们通过使用不同的黑盒优化技术放宽epivoimume约束来研究此类点集的差异，并通过数值来优化预期的差异。
Classical jittered sampling partitions $[0,1]^d$ into $m^d$ cubes for a positive integer $m$ and randomly places a point inside each of them, providing a point set of size $N=m^d$ with small discrepancy. The aim of this note is to provide a construction of partitions that works for arbitrary $N$ and improves straight-forward constructions. We show how to construct equivolume partitions of the $d$-dimensional unit cube with hyperplanes that are orthogonal to the main diagonal of the cube. We investigate the discrepancy of such point sets and optimise the expected discrepancy numerically by relaxing the equivolume constraint using different black-box optimisation techniques.
