BAYESIAN NONPARAMETRIC INFERENCE ON THE STIEFEL MANIFOLD
BAYESIAN NONPARAMETRIC INFERENCE ON THE STIEFEL MANIFOLD
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DOI：
10.5705/ss.202016.0017
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发表时间：
2017-04-01
影响因子：
1.4
通讯作者：
Dunson, David
中科院分区：
文献类型：
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作者：
Lin, Lizhen;Rao, Vinayak;Dunson, David
Stiefel流形V-p，V-d是所有d×p正交阵的空间，这里的d-1超和所有正交阵的空间构成特例。在对位于Stiefel流形上的数据进行建模时，经常使用参数分布，例如矩阵朗之万分布；然而，模型错误指定是一个令人担忧的问题，并且希望有非参数替代。目前的非参数方法主要是基于Frechet-Mean的。我们采用完全生成的非参数方法，它依赖于混合参数核，如矩阵的朗之万法。所提出的核混合可以逼近Stiefel流形上的一大类分布，并且我们发展了证明后验一致性的理论。虽然已经有了发展一般后验一致性结果的工作，但将这些结果推广到这个特定流形需要大量的新理论。后验推断以近地天体的数据集为例进行了说明。
The Stiefel manifold V-p,V-d is the space of all d x p orthonormal matrices, with the d-1 hypersp here 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 Frechet-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.