[1] 
J. Garcke.
A dimension adaptive combination technique using localised adaptation
criteria.
In H. G. Bock, X. P. Hoang, R. Rannacher, and J. P. SchlĂ¶der,
editors, Modeling, Simulation and Optimization of Complex Processes,
pages 115125. Springer Berlin Heidelberg, 2012. [ bib  DOI  http  .pdf 1 ] We present a dimension adaptive sparse grid combination technique for the machine learning problem of regression. A function over a d dimensional space, which assumedly describes the relationship between the features and the response variable, is reconstructed using a linear combination of partial functions; these may depend only on a subset of all features. The partial functions, which are piecewise multilinear, are adaptively chosen during the computational procedure. This approach (approximately) identifies the anova decomposition of the underlying problem. We introduce two new localized criteria, one inspired by residual estimators based on a hierarchical subspace decomposition, for the dimension adaptive grid choice and investigate their performance on real data.
