@InProceedings{ Garcke:2007*1, author = {Jochen Garcke}, title = {A dimension adaptive sparse grid combination technique for machine learning}, booktitle = { Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006}, year = {2007}, editor = {Wayne Read and Jay W. Larson and A. J. Roberts}, volume = {48}, series = {ANZIAM J.}, pages = {C725--C740}, abstract = {We introduce a dimension adaptive sparse grid combination technique for the machine learning problems of classification and 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 that possibly depend only on a subset of all features. The partial functions are adaptively chosen during the computational procedure. This approach (approximately) identifies the \textsc{anova}-decomposition of the underlying problem. Experiments on synthetic data, where the structure is known, show the advantages of a dimension adaptive combination technique in run time behaviour, approximation errors, and interpretability. }, annote = {other}, file = {dimAdapCTAC.pdf:http\://www.math.tu-berlin.de/~garcke/paper/dimAdapCTAC.pdf:PDF} , http = {http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/70} , pdf = {http://garcke.ins.uni-bonn.de/research/pub/dimAdapCTAC.pdf} }