  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.
