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A dimension adaptive combination technique using localised adaptation criteria

: Garcke, J.


Bock, H.G.:
Modeling, simulation and optimization of complex processes : Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2 - 6, 2009, Hanoi, Vietnam
Berlin: Springer, 2012
ISBN: 978-3-642-25706-3
ISBN: 3-642-25706-2
ISBN: 978-3-642-25707-0
International Conference on High Performance Scientific Computing <4, 2009, Hanoi>
Fraunhofer SCAI ()

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.