Fitting multidimensional data using gradient penalties and the sparse grid combination technique
Please always quote using this URN:urn:nbn:de:0296-matheon-5356
- Sparse grids, combined with gradient penalties provide an attractive tool for regularised least squares fitting. It has earlier been found that the combination technique, which builds a sparse grid function using a linear combination of approximations on partial grids, is here not as effective as it is in the case of elliptic partial differential equations. We argue that this is due to the irregular and random data distribution, as well as the proportion of the number of data to the grid resolution. These effects are investigated both in theory and experiments. As part of this investigation we also show how overfitting arises when the mesh size goes to zero. We conclude with a study of modified ``optimal'' combination coefficients who prevent the amplification of the sampling noise present while using the original combination coefficients.
Author: | Jochen Garcke, Markus Hegland |
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URN: | urn:nbn:de:0296-matheon-5356 |
Referee: | Harry Yserentant |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/05/03 |
Release Date: | 2008/11/26 |
Tag: | |
MSC-Classification: | 62-XX STATISTICS / 62Gxx Nonparametric inference / 62G08 Nonparametric regression |
62-XX STATISTICS / 62Jxx Linear inference, regression / 62J02 General nonlinear regression | |
65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D10 Smoothing, curve fitting | |
Preprint Number: | 568 |