Bayesian nonparametric inference on the stiefel manifold
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
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Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 0801 Artificial Intelligence and Image Processing
- 0199 Other Mathematical Sciences
- 0104 Statistics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 0801 Artificial Intelligence and Image Processing
- 0199 Other Mathematical Sciences
- 0104 Statistics