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Online Sparse Matrix Gaussian Process Regression and Vision Applications

  • Ananth Ranganathan
  • Ming-Hsuan Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5302)

Abstract

We present a new Gaussian Process inference algorithm, called Online Sparse Matrix Gaussian Processes (OSMGP), and demonstrate its merits with a few vision applications. The OSMGP is based on the observation that for kernels with local support, the Gram matrix is typically sparse. Maintaining and updating the sparse Cholesky factor of the Gram matrix can be done efficiently using Givens rotations. This leads to an exact, online algorithm whose update time scales linearly with the size of the Gram matrix. Further, if approximate updates are permissible, the Cholesky factor can be maintained at a constant size using hyperbolic rotations to remove certain rows and columns corresponding to discarded training examples. We demonstrate that, using these matrix downdates, online hyperparameter estimation can be included without affecting the linear runtime complexity of the algorithm. The OSMGP algorithm is applied to head-pose estimation and visual tracking problems. Experimental results demonstrate that the proposed method is accurate, efficient and generalizes well using online learning.

Keywords

Online Learning Inertia Measurement Unit Sparse Matrix Radial Basis Function Kernel Training Point 
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.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ananth Ranganathan
    • 1
  • Ming-Hsuan Yang
    • 2
  1. 1.Honda Research InstituteUSA
  2. 2.University of CaliforniaMercedUSA

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