Additive models in high dimensions

Details Additive models in high dimensions Additive models in high dimensions

1999-12-30

arxiv.org/abs/cs/9912020v2

Proc. of 12th Computational Techniques and Applications Conference, CTAC-2004 (Rob May and A.J. Roberts, eds.), ANZIAM J. 46 (

Computer Science

Data Structures and Algorithms

LaTeX 2e document, 21 pages, 5 figures

Scientific paper

We discuss some aspects of approximating functions on high-dimensional data sets with additive functions or ANOVA decompositions, that is, sums of functions depending on fewer variables each. It is seen that under appropriate smoothness conditions, the errors of the ANOVA decompositions are of order $O(n^{m/2})$ for approximations using sums of functions of up to $m$ variables under some mild restrictions on the (possibly dependent) predictor variables. Several simulated examples illustrate this behaviour.

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