Abstract

Sparse grids, as studied by Zenger and Griebel in the last 10 years have been a very successful in the solution of partial differential equations, integral equations and classification problems with up to around 10 dimensions. We will discuss a general framework which allows to extend the method to the case of nominal and mixed variables and to very high dimensions. An implementation which demonstrates the concept will be discussed and compared to classical sparse grids and full grids. In particular, we will discuss the adaptive approximation in a function space lattice. We have observed that the adaptive method can recover ANOVA decompositions of the function and thus has the additional advantage of being comprehensible which is an important condition for data mining applications.

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