Approximation of generalized ridge functions in high dimensions

JOURNAL OF APPROXIMATION THEORY

卷:245

Article

Keiper, Sandra¹ 

[1] Tech Univ Berlin, Dept Math, D-10623 Berlin, Germany

关键词: Ridge functions;    Function approximation;    Big data;    High dimensions;    Active variables;    Active subspaces;    Optimization over Grassmannian manifolds;   

DOI  :  10.1016/j.jat.2019.04.006

来源: Elsevier

【 摘 要 】

This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of R-N. We introduce the notion of linear-sleeve functions, whose function values only depend on the distance to some unknown linear subspace L. We propose two effective algorithms to approximate linear-sleeve functions f (x) = g(dist(x, L)(2)), when both the linear subspace L subset of R-N and the function g is an element of C-s[0, 1] are unknown. We will prove error bounds for both algorithms and provide an extensive numerical comparison of both. We further propose an approach of how to apply these algorithms to capture general sleeve functions, which are constant along some lower dimensional submanifolds. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free