Research Group of Prof. Dr. J. Garcke
Institute for Numerical Simulation

  author = {Garcke, Jochen},
  affiliation = {Institut für Mathematik, MA 3-3, Technische Universität
		  Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany},
  title = {A Dimension Adaptive Combination Technique Using Localised
		  Adaptation Criteria},
  booktitle = {Modeling, Simulation and Optimization of Complex
  editor = {Bock, Hans Georg and Hoang, Xuan Phu and Rannacher, Rolf
		  and Schlöder, Johannes P.},
  publisher = {Springer Berlin Heidelberg},
  isbn = {978-3-642-25707-0},
  keyword = {Mathematics and Statistics},
  pages = {115-125},
  url = {},
  doi = {10.1007/978-3-642-25707-0_10},
  abstract = {We present a dimension adaptive sparse grid combination
		  technique for the machine learning problem of 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; these may depend only on
		  a subset of all features. The partial functions, which are
		  piecewise multilinear, are adaptively chosen during the
		  computational procedure. This approach (approximately)
		  identifies the anova -decomposition of the underlying
		  problem. We introduce two new localized criteria, one
		  inspired by residual estimators based on a hierarchical
		  subspace decomposition, for the dimension adaptive grid
		  choice and investigate their performance on real data.},
  year = {2012},
  annote = {other},
  pdf = { 1}