Research Group of Prof. Dr. J. Garcke
Institute for Numerical Simulation
[1] S. Börm and J. Garcke. Approximating gaussian processes with H2-matrices. In J. N. Kok, J. Koronacki, R. L. de Mantaras, S. Matwin, D. Mladen, and A. Skowron, editors, Proceedings of 18th European Conference on Machine Learning, Warsaw, Poland, September 17-21, 2007. ECML 2007, volume 4701, pages 42-53, 2007.
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To compute the exact solution of Gaussian process regression one needs (N3) computations for direct and (N2) for iterative methods since it involves a densely populated kernel matrix of size N ×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 H2-matrix. This matrix can be represented by only O(N m) units of storage, where m is a parameter controlling the accuracy of the approximation, while the computation of the H2-matrix scales with O(N m logN). Practical experiments demonstrate that our scheme leads to significant reductions in storage requirements and computing times for large data sets in lower dimensional spaces.