A dimension adaptive sparse grid combination technique for machine
In W. Read, J. W. Larson, and A. J. Roberts, editors,
Proceedings of the 13th Biennial Computational Techniques and Applications
Conference, CTAC-2006, volume 48 of ANZIAM J., pages C725-C740, 2007.
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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 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.