A dimension adaptive sparse grid combination technique for machine learning

Jochen Garcke

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.

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DOI: http://dx.doi.org/10.21914/anziamj.v48i0.70



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