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Sparse Bayesian infinite factor models.

Publication ,  Journal Article
Bhattacharya, A; Dunson, DB
Published in: Biometrika
June 2011

We focus on sparse modelling of high-dimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameter-expanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs sampler that scales well as data dimensionality increases. The gain in efficiency is achieved by the joint conjugacy property of the proposed prior, which allows block updating of the loadings matrix. We propose an adaptive Gibbs sampler for automatically truncating the infinite loading matrix through selection of the number of important factors. Theoretical results are provided on the support of the prior and truncation approximation bounds. A fast algorithm is proposed to produce approximate Bayes estimates. Latent factor regression methods are developed for prediction and variable selection in applications with high-dimensional correlated predictors. Operating characteristics are assessed through simulation studies, and the approach is applied to predict survival times from gene expression data.

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Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

June 2011

Volume

98

Issue

2

Start / End Page

291 / 306

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

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Bhattacharya, A., & Dunson, D. B. (2011). Sparse Bayesian infinite factor models. Biometrika, 98(2), 291–306. https://doi.org/10.1093/biomet/asr013
Bhattacharya, A., and D. B. Dunson. “Sparse Bayesian infinite factor models.Biometrika 98, no. 2 (June 2011): 291–306. https://doi.org/10.1093/biomet/asr013.
Bhattacharya A, Dunson DB. Sparse Bayesian infinite factor models. Biometrika. 2011 Jun;98(2):291–306.
Bhattacharya, A., and D. B. Dunson. “Sparse Bayesian infinite factor models.Biometrika, vol. 98, no. 2, June 2011, pp. 291–306. Epmc, doi:10.1093/biomet/asr013.
Bhattacharya A, Dunson DB. Sparse Bayesian infinite factor models. Biometrika. 2011 Jun;98(2):291–306.
Journal cover image

Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

June 2011

Volume

98

Issue

2

Start / End Page

291 / 306

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics