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Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

Bo Chen1, Minhua Chen1, John Paisley1, Aimee Zaas2, Christopher Woods2, Geoffrey S Ginsburg2, Alfred Hero3, Joseph Lucas2, David Dunson4 and Lawrence Carin1*

Author Affiliations

1 Electrical and Computer Engineering Department, Duke University, Durham, NC, USA

2 Institute for Genome Sciences & Policy, Department of Medicine Duke University, Durham, NC, USA

3 Electrical & Computer Engineering Department, University of Michigan, Ann Arbor, MI, USA

4 Statistics Department, Duke University, Durham, NC, USA

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BMC Bioinformatics 2010, 11:552  doi:10.1186/1471-2105-11-552

Published: 9 November 2010



Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis.


Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches.


Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.