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Bayesian Compressed Regression

Publication ,  Journal Article
Guhaniyogi, R; Dunson, DB
Published in: Journal of the American Statistical Association
October 2, 2015

As an alternative to variable selection or shrinkage in high-dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low-dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the compressed data is available analytically, speeding up computation by many orders of magnitude while also bypassing robustness issues due to convergence and mixing problems with MCMC. Model averaging is used to reduce sensitivity to the random projection matrix, while accommodating uncertainty in the subspace dimension. Strong theoretical support is provided for the approach by showing near parametric convergence rates for the predictive density in the large p small n asymptotic paradigm. Practical performance relative to competitors is illustrated in simulations and real data applications.

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Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 2, 2015

Volume

110

Issue

512

Start / End Page

1500 / 1514

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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Guhaniyogi, R., & Dunson, D. B. (2015). Bayesian Compressed Regression. Journal of the American Statistical Association, 110(512), 1500–1514. https://doi.org/10.1080/01621459.2014.969425
Guhaniyogi, R., and D. B. Dunson. “Bayesian Compressed Regression.” Journal of the American Statistical Association 110, no. 512 (October 2, 2015): 1500–1514. https://doi.org/10.1080/01621459.2014.969425.
Guhaniyogi R, Dunson DB. Bayesian Compressed Regression. Journal of the American Statistical Association. 2015 Oct 2;110(512):1500–14.
Guhaniyogi, R., and D. B. Dunson. “Bayesian Compressed Regression.” Journal of the American Statistical Association, vol. 110, no. 512, Oct. 2015, pp. 1500–14. Scopus, doi:10.1080/01621459.2014.969425.
Guhaniyogi R, Dunson DB. Bayesian Compressed Regression. Journal of the American Statistical Association. 2015 Oct 2;110(512):1500–1514.

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 2, 2015

Volume

110

Issue

512

Start / End Page

1500 / 1514

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics