@InProceedings{ Boerm.Garcke:2007, author = {S. B\"orm and J. Garcke}, title = {Approximating Gaussian Processes with ${H^2}$-matrices}, booktitle = {Proceedings of 18th European Conference on Machine Learning, Warsaw, Poland, September 17-21, 2007. ECML 2007}, year = {2007}, editor = {Joost N. Kok and Jacek Koronacki and Ramon Lopez de Mantaras and Stan Matwin and Dunja Mladen and Andrzej Skowron}, volume = {4701}, pages = {42--53}, abstract = {To compute the exact solution of Gaussian process regression one needs $\Os(N^3)$ computations for direct and $\Os(N^2)$ for iterative methods since it involves a densely populated kernel matrix of size $N \times N$, here $N$ denotes the number of data. This makes large scale learning problems intractable by standard techniques. We propose to use an alternative approach: the kernel matrix is replaced by a data-sparse approximation, called an ${\mathcal H}^2$-matrix. This matrix can be represented by only ${\cal O}(N m)$ units of storage, where $m$ is a parameter controlling the accuracy of the approximation, while the computation of the ${\mathcal H}^2$-matrix scales with ${\cal O}(N m \log N)$. Practical experiments demonstrate that our scheme leads to significant reductions in storage requirements and computing times for large data sets in lower dimensional spaces.}, annote = {proc_ref}, doi = {10.1007/978-3-540-74958-5_8}, file = {gpWithH2.pdf:http\://www.math.tu-berlin.de/~garcke/paper/gpWithH2.pdf:PDF} , pdf = {http://garcke.ins.uni-bonn.de/research/pub/gpWithH2.pdf}, seriestitle = { Lecture Notes in Artificial Intelligence} }