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Bayesian nonparametric inference on the stiefel manifold

Publication ,  Journal Article
Lin, L; Rao, V; Dunson, D
Published in: Statistica Sinica
April 1, 2017

The Stiefel manifold Vp,d is the space of all d × p orthonormal matrices, with the d-1 hypersphere and the space of all orthogonal matrices constituting special cases. In modeling data lying on the Stiefel manifold, parametric distributions such as the matrix Langevin distribution are often used; however, model misspecification is a concern and it is desirable to have nonparametric alternatives. Current nonparametric methods are mainly Fŕechet-mean based. We take a fully generative nonparametric approach, which relies on mixing parametric kernels such as the matrix Langevin. The proposed kernel mixtures can approximate a large class of distributions on the Stiefel manifold, and we develop theory showing posterior consistency. While there exists work developing general posterior consistency results, extending these results to this particular manifold requires substantial new theory. Posterior inference is illustrated on a dataset of near-Earth objects.

Duke Scholars

Published In

Statistica Sinica

DOI

ISSN

1017-0405

Publication Date

April 1, 2017

Volume

27

Issue

2

Start / End Page

535 / 553

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0801 Artificial Intelligence and Image Processing
  • 0199 Other Mathematical Sciences
  • 0104 Statistics
 

Citation

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MLA
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Lin, L., Rao, V., & Dunson, D. (2017). Bayesian nonparametric inference on the stiefel manifold. Statistica Sinica, 27(2), 535–553. https://doi.org/10.5705/ss.202016.0017
Lin, L., V. Rao, and D. Dunson. “Bayesian nonparametric inference on the stiefel manifold.” Statistica Sinica 27, no. 2 (April 1, 2017): 535–53. https://doi.org/10.5705/ss.202016.0017.
Lin L, Rao V, Dunson D. Bayesian nonparametric inference on the stiefel manifold. Statistica Sinica. 2017 Apr 1;27(2):535–53.
Lin, L., et al. “Bayesian nonparametric inference on the stiefel manifold.” Statistica Sinica, vol. 27, no. 2, Apr. 2017, pp. 535–53. Scopus, doi:10.5705/ss.202016.0017.
Lin L, Rao V, Dunson D. Bayesian nonparametric inference on the stiefel manifold. Statistica Sinica. 2017 Apr 1;27(2):535–553.

Published In

Statistica Sinica

DOI

ISSN

1017-0405

Publication Date

April 1, 2017

Volume

27

Issue

2

Start / End Page

535 / 553

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0801 Artificial Intelligence and Image Processing
  • 0199 Other Mathematical Sciences
  • 0104 Statistics