Models of random sparse eigenmatrices and Bayesian analysis of multivariate structure

Conference Paper

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for defining distributions on sparsity structure of random eigenmatrices. We explore theoretical aspects and implications for conditional independence structures arising in multivariate Gaussian models, and discuss connections with sparse PCA, factor analysis and Gaussian graphical models. Methodology includes model-based exploratory data analysis and Bayesian analysis via reversible jump Markov chain Monte Carlo. A simulation study examines the ability to identify sparse multivariate structures compared to the benchmark graphical modelling approach. Extensions to multivariate normal mixture models with additional measurement errors move into the framework of latent structure analysis of broad practical interest. We explore the implications and utility of the new models with summaries of a detailed applied study of a 20-dimensional breast cancer genomics data set.

Full Text

Duke Authors

Cited Authors

  • Cron, A; West, M

Published Date

  • January 1, 2016

Published In

Volume / Issue

  • 11 /

Start / End Page

  • 125 - 153

Electronic International Standard Serial Number (EISSN)

  • 2197-8549

International Standard Serial Number (ISSN)

  • 2193-2808

International Standard Book Number 13 (ISBN-13)

  • 9783319270975

Digital Object Identifier (DOI)

  • 10.1007/978-3-319-27099-9_7

Citation Source

  • Scopus