Simulation of the Matrix Bingham–von Mises–Fisher Distribution, With Applications to Multivariate and Relational Data

By Peter D. Hoff. 2007

224 citations recorded by the source corpus.

Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham–von Mises–Fisher distribution is a probability distribution on the set of orthonormal matrices that includes linear and quadratic terms in the log-density, and arises as a posterior distribution in latent factor models for multivariate and relational data. This article describes rejection and Gibbs sampling algorithms for sampling from this family of distributions, and illustrates their use in the analysis of a protein–protein interaction network. Supplemental materials, including code and data to generate all of the numerical results in this article, are available online.

Subfields: Molecular Biology, Radiology, Nuclear Medicine and Imaging

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Molecular Biology

1. Yue Wang
2. Leting Wu
3. Aarti Singh
4. Zhihua Su
5. S. Pal
6. Kshitij Khare
7. Kamalika Chaudhuri
8. Kaushik Sinha

In Radiology, Nuclear Medicine and Imaging

1. Yue Wang
2. Leting Wu
3. Aarti Singh
4. Zhihua Su
5. S. Pal
6. Kshitij Khare
7. Kamalika Chaudhuri
8. Kaushik Sinha

Citations in the corpus

• Near-optimal Differentially Private Principal Components (2012, background): “A randomized algorithm A(·) is an (⇢, ⌘)-close approximation to the top eigenvector if for all data sets D of n points, P (q A (A(D)) ⇢) 1 ⌘, (5) where the probability is taken over A(·).”
• Differential Privacy Preserving Spectral Graph Analysis (2013, methodology): “The sampling scheme by Hoff [7] ensures Lemma 1 to approximate inferences for U and Λ for a given graph topology.”
• Differentially private subspace clustering (2015, background): “(12) is a special case of the matrix Bingham distribution, which admits a Gibbs sampler [16].”
• A Bayesian approach for envelope models (2017, methodology): “Hoff [8] provides a rejection sampling method to generate samples from the matrix Bingham distribution on S2,2.”
• Near-Optimal Algorithms for Differentially-Private Principal Components (2012, methodology): “rom the distribution specied by the exponential mechanism may be expensive computationally, especially for continuous-valued outputs. We implement PPCA using a recently-proposed Gibbs sampler due to Ho (2009). Gibbs sampling is a popular Markov Chain Monte Carlo (MCMC) technique in which samples are”