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.

当多元函数不依赖于其所有变量时，可以从比其他要求更少的点评估中得出近似值。例如，在目标功能为Lipschitz的情况下，已经对此进行了量化。本说明在目标功能的其他假设下研究了相同的问题。如果它是线性的或二次方的，则利用与压缩感测的连接来确定准确恢复它所需的点评估次数。如果以坐标方式递增，那么将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次数。特别强调明确的评估点集和实用的恢复方法。