Learning multivariate functions with low-dimensional structures using polynomial bases
Numerical Analysis
2022-01-31 v4 Numerical Analysis
Abstract
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of variance (ANOVA) decomposition. For functions with a low-dimensional structure, i.e., a low superposition dimension, we are able to achieve a reconstruction from scattered data and simultaneously understand relationships between different variables.
Cite
@article{arxiv.1912.03195,
title = {Learning multivariate functions with low-dimensional structures using polynomial bases},
author = {Daniel Potts and Michael Schmischke},
journal= {arXiv preprint arXiv:1912.03195},
year = {2022}
}