Adaptive sparse grids

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. It is seen that 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 can thus provide comprehensible models which is very important for data mining applications. Maybe 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.