Loading…

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; ho...

Full description

Saved in:
Bibliographic Details
Published in:Statistica Sinica 2017-04, Vol.27 (2), p.535-553
Main Authors: Lin, Lizhen, Rao, Vinayak, Dunson, David
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 Fréchet-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.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.202016.0017