Sampling schemes and recovery algorithms for functions of few coordinate variables
Sampling schemes and recovery algorithms for functions of few coordinate variables
复制标题
少坐标变量函数的采样方案和恢复算法
DOI：
10.1016/j.jco.2019.101457
复制
发表时间：
2020
影响因子：
1.7
通讯作者：
Foucart, Simon
中科院分区：
文献类型：
--
作者：
Foucart, Simon
当一个多变量函数不依赖于它的所有变量时，它可以从比其他情况下所需的更少的点计算中近似。这在之前已经被量化，例如在目标函数是Lipschitz的情况下。本说明在目标函数的其他假设下考察了相同的问题。如果它是线性的或二次的，则利用与压缩感知的连接，以便确定精确恢复它所需的点评估的数量。如果它是坐标递增的，则利用与组测试的连接来确定恢复活动变量集所需的点评估的数量。特别强调的是明确的评价点集和实用的恢复方法。本文的结果也为群体测试领域的研究做出了新的贡献。
When a multivariate function does not depend on all of its variables, it can be approximated from fewer point evaluations than otherwise required. This has been previously quantified e.g. in the case where the target function is Lipschitz. This note examines the same problem under other assumptions on the target function. If it is linear or quadratic, then connections to compressive sensing are exploited in order to determine the number of point evaluations needed for recovering it exactly. If it is coordinatewise increasing, then connections to group testing are exploited in order to determine the number of point evaluations needed for recovering the set of active variables. A particular emphasis is put on explicit sets of evaluation points and on practical recovery methods. The results presented here also add a new contribution to the field of group testing.
联合低秩和双稀疏恢复：问题和部分答案
影响因子：
2.2
作者：
Foucart, Simon;Gribonval, Rémi;Jacques, Laurent;Rauhut, Holger
通讯作者：
Rauhut, Holger
影响因子：
2.7
作者：
R. DeVore;G. Petrova;P. Wojtaszczyk
通讯作者：
P. Wojtaszczyk
影响因子：
1.7
作者：
P. Wojtaszczyk
通讯作者：
P. Wojtaszczyk