Approximating Gaussian Processes with \({\cal H}^2\)-Matrices

  • Steffen Börm
  • Jochen Garcke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4701)


To compute the exact solution of Gaussian process regression one needs \(\mathcal{O}(N^3)\) computations for direct and \(\mathcal{O}(N^2)\) 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 \({\mathcal H}^2\)-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.


Gaussian Process Kernel Matrix Gaussian Process Regression Linear Equation System Mote22 Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Steffen Börm
    • 1
  • Jochen Garcke
    • 2
  1. 1.Max Planck Institute for Mathematics in the Sciences, Inselstraße 22–26, 04103 LeipzigGermany
  2. 2.Technische Universität Berlin, Institut für Mathematik, MA 3-3, Straße des 17. Juni 136, 10623 Berlin 

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