A dimension adaptive sparse grid combination technique for machine learning
DOI:
https://doi.org/10.21914/anziamj.v48i0.70Abstract
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. References- M. Griebel, M. Schneider, and C. Zenger. A combination technique for the solution of sparse grid problems. In P. de Groen and R. Beauwens, editors, Iterative Methods in Linear Algebra, pages 263--281. IMACS, Elsevier, North Holland, 1992. http://wissrech.ins.uni-bonn.de/research/pub/griebel/griesiam.ps.gz.
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Published
2007-12-27
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Section
Proceedings Computational Techniques and Applications Conference