Learning multivariate functions with low-dimensional structures using polynomial bases

Understand

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.