Learning high-dimensional additive models on the torus

07/26/2019

∙

by   Daniel Potts, et al.

∙

0

∙

share

In this paper we study the multivariate ANOVA decomposition for 1-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in L_∞ and L_2. We present an approximation method based on the truncated decomposition with regard to a superposition dimension d_s.