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Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process

Publication ,  Conference
Wang, Y; Dunson, D
Published in: Advances in Neural Information Processing Systems
January 1, 2015

Learning of low dimensional structure in multidimensional data is a canonical problem in machine learning. One common approach is to suppose that the observed data are close to a lower-dimensional smooth manifold. There are a rich variety of manifold learning methods available, which allow mapping of data points to the manifold. However, there is a clear lack of probabilistic methods that allow learning of the manifold along with the generative distribution of the observed data. The best attempt is the Gaussian process latent variable model (GP-LVM), but identifiability issues lead to poor performance. We solve these issues by proposing a novel Coulomb repulsive process (Corp) for locations of points on the manifold, inspired by physical models of electrostatic interactions among particles. Combining this process with a GP prior for the mapping function yields a novel electrostatic GP (electroGP) process. Focusing on the simple case of a one-dimensional manifold, we develop efficient inference algorithms, and illustrate substantially improved performance in a variety of experiments including filling in missing frames in video.

Duke Scholars

Published In

Advances in Neural Information Processing Systems

ISSN

1049-5258

Publication Date

January 1, 2015

Volume

2015-January

Start / End Page

1738 / 1746

Related Subject Headings

  • 4611 Machine learning
  • 1702 Cognitive Sciences
  • 1701 Psychology
 

Citation

APA
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ICMJE
MLA
NLM
Wang, Y., & Dunson, D. (2015). Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process. In Advances in Neural Information Processing Systems (Vol. 2015-January, pp. 1738–1746).
Wang, Y., and D. Dunson. “Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process.” In Advances in Neural Information Processing Systems, 2015-January:1738–46, 2015.
Wang Y, Dunson D. Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process. In: Advances in Neural Information Processing Systems. 2015. p. 1738–46.
Wang, Y., and D. Dunson. “Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process.” Advances in Neural Information Processing Systems, vol. 2015-January, 2015, pp. 1738–46.
Wang Y, Dunson D. Probabilistic curve learning: Coulomb repulsion and the electrostatic Gaussian process. Advances in Neural Information Processing Systems. 2015. p. 1738–1746.

Published In

Advances in Neural Information Processing Systems

ISSN

1049-5258

Publication Date

January 1, 2015

Volume

2015-January

Start / End Page

1738 / 1746

Related Subject Headings

  • 4611 Machine learning
  • 1702 Cognitive Sciences
  • 1701 Psychology