@Article{	  Garcke.Hegland:2009,
  author	= {Jochen Garcke and Markus Hegland},
  title		= {Fitting multidimensional data using gradient penalties and
		  the sparse grid combination technique},
  journal	= {Computing},
  year		= {2009},
  volume	= {84},
  pages		= {1--25},
  number	= {1-2},
  month		= {April},
  abstract	= {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.},
  annote	= {journal},
  doi		= {10.1007/s00607-009-0027-x},
  issn		= {0010-485X (Print) 1436-5057 (Online)},
  keywords	= {Sparse grids - Combination technique - Regression -
		  High-dimensional data - Regularisation},
  pdf		= {http://garcke.ins.uni-bonn.de/research/pub/fitdata_gradient.pdf}
		  ,
  publisher	= {Springer Wien},
  subject_collection={Mathematics and Statistics},
  url		= {http://www.springerlink.com/content/128074u22765g76r/}
}