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首页> 外文期刊>Journal of complexity >The recovery of ridge functions on the hypercube suffers from the curse of dimensionality
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The recovery of ridge functions on the hypercube suffers from the curse of dimensionality

机译：在HyperCube上恢复脊功能的职能遭受了维度的诅咒

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摘要

A multivariate ridge function is a function of the form f (x) = g(a(T) x), where g is univariate and a is an element of R-d. We show that the recovery of an unknown ridge function defined on the hypercube [-1, 1](d) with Lipschitz-regular profile g suffers from the curse of dimensionality when the recovery error is measured in the L-infinity-norm, even if we allow randomized algorithms. If a limited number of components of a is substantially larger than the others, then the curse of dimensionality is not present and the problem is weakly tractable, provided the profile g is sufficiently regular. (C) 2020 Elsevier Inc. All rights reserved.
机译：多元脊函数是F（x）= g（a（t）x）的形式的函数，其中g是单变量，a是R-D的元素。我们表明，当在LIPSCHITZ-FIRMING-REVITION-NORM中测量恢复误差时，HyperCube [-1,1]（d）上定义的未知脊函数的恢复遭受了维度的诅咒，甚至如果我们允许随机算法。如果A的有限数量的组分基本上大于其他组件，则不存在维度的诅咒，并且该问题是弱易易透视的。 （c）2020 Elsevier Inc.保留所有权利。

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