Learning multivariate functions with low-dimensional structures using polynomial bases
share
In this paper we study the multivariate ANOVA decomposition for functions over the unit cube with respect to complete orthonormal systems of polynomials. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. We present a method that uses this decomposition as a tool to understand and learn the structure of high-dimensional functions, i.e., which dimensions and dimension interactions are important. The functions we consider are either exactly or approximately of a low-dimensional structure, i.e., the number of simultaneous dimension interactions is effectively low. The structural knowledge of the function is then used to find an approximation.
READ FULL TEXT