A Dimension Adaptive Combination Technique Using Localised Adaptation Criteria

Jochen Garcke ()
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Jochen Garcke: Technische Universität Berlin, Institut für Mathematik, MA 3-3

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2012, pp 115-125 from Springer

Abstract: 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25707-0_10

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DOI: 10.1007/978-3-642-25707-0_10

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