A dimension adaptive combination technique using localised adaptation
In H. G. Bock, X. P. Hoang, R. Rannacher, and J. P. Schlöder,
editors, Modeling, Simulation and Optimization of Complex Processes,
pages 115-125. Springer Berlin Heidelberg, 2012.
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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.