TY - GEN A1 - Garcke, Jochen A1 - Hegland, Markus T1 - Fitting multidimensional data using gradient penalties and the sparse grid combination technique N2 - 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. KW - sparse grids KW - combination technique KW - regression KW - high-dimensional data KW - regularisation Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/535 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5356 ER -