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

  author = {Jochen Garcke},
  title = {Regression with the optimised combination technique},
  booktitle = {Proceedings of the 23rd ICML '06},
  year = {2006},
  editor = {W. Cohen and A. Moore},
  pages = {321--328},
  address = {New York, NY, USA},
  publisher = {ACM Press},
  abstract = {We consider the sparse grid combination technique for
		  regression, which we regard as a problem of function
		  reconstruction in some given function space. We use a
		  regularised least squares approach, discretised by sparse
		  grids and solved using the so-called combination technique,
		  where a certain sequence of conventional grids is employed.
		  The sparse grid solution is then obtained by addition of
		  the partial solutions with combination coefficients
		  dependent on the involved grids. This approach shows
		  instabilities in certain situations and is not guaranteed
		  to converge with higher discretisation levels. In this
		  article we apply the recently introduced optimised
		  combination technique, which repairs these instabilities.
		  Now the combination coefficients also depend on the
		  function to be reconstructed, resulting in a non-linear
		  approximation method which achieves very competitive
		  results. We show that the computational complexity of the
		  improved method still scales only linear in the number of
		  data. },
  annote = {proc_ref},
  doi = {doi:10.1145/1143844.1143885},
  file = {regressionOpticomICML06.pdf:http\://},
  location = {Pittsburgh, Pennsylvania},
  pdf = { 1}