@InCollection{ Garcke:2012, author = {Garcke, Jochen}, affiliation = {Institut für Mathematik, MA 3-3, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany}, title = {A Dimension Adaptive Combination Technique Using Localised Adaptation Criteria}, booktitle = {Modeling, Simulation and Optimization of Complex Processes}, editor = {Bock, Hans Georg and Hoang, Xuan Phu and Rannacher, Rolf and Schlöder, Johannes P.}, publisher = {Springer Berlin Heidelberg}, isbn = {978-3-642-25707-0}, keyword = {Mathematics and Statistics}, pages = {115-125}, url = {http://dx.doi.org/10.1007/978-3-642-25707-0_10}, doi = {10.1007/978-3-642-25707-0_10}, abstract = {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.}, year = {2012}, annote = {other}, pdf = {http://garcke.ins.uni-bonn.de/research/pub/dimadapLocalHPSC.pdf} }