Bayesian nonparametric inference on the stiefel manifold

Published

Journal Article

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 FÅ•echet-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.

Full Text

Duke Authors

Cited Authors

  • Lin, L; Rao, V; Dunson, D

Published Date

  • April 1, 2017

Published In

Volume / Issue

  • 27 / 2

Start / End Page

  • 535 - 553

International Standard Serial Number (ISSN)

  • 1017-0405

Digital Object Identifier (DOI)

  • 10.5705/ss.202016.0017

Citation Source

  • Scopus