Adaptive sparse grids

Abstract

Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial differential equations, integral equations and classification problems. Adaptive sparse grid functions are elements of a function space lattice. Such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions with categorical and continuous variables. We have observed in first tests that these general adaptive sparse grids allow the identification of the ANOVA structure and thus provide comprehensible models. This is very important for data mining applications. Perhaps the main advantage of these models is that they do not include any spurious interaction terms and thus can deal with very high dimensional data.