Research Group of Prof. Dr. J. Garcke
Institute for Numerical Simulation
[1] J. Garcke. A dimension adaptive sparse grid combination technique for machine learning. 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.