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Bayesian regularization via graph Laplacian

Publication ,  Journal Article
Liu, F; Chakraborty, S; Li, F; Liu, Y; Lozano, AC
Published in: Bayesian Analysis
January 1, 2014

Regularization plays a critical role in modern statistical research, especially in high-dimensional variable selection problems. Existing Bayesian methods usually assume independence between variables a priori. In this article, we propose a novel Bayesian approach, which explicitly models the dependence structure through a graph Laplacian matrix. We also generalize the graph Laplacian to allow both positively and negatively correlated variables. A prior distribution for the graph Laplacian is then proposed, which allows conjugacy and thereby greatly simplifies the computation. We show that the proposed Bayesian model leads to proper posterior distribution. Connection is made between our method and some existing regularization methods, such as Elastic Net, Lasso, Octagonal Shrinkage and Clustering Algorithm for Regression (OSCAR) and Ridge regression. An efficient Markov Chain Monte Carlo method based on parameter augmentation is developed for posterior computation. Finally, we demonstrate the method through several simulation studies and an application on a real data set involving key performance indicators of electronics companies. © 2014 International Society for Bayesian Analysis.

Duke Scholars

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

January 1, 2014

Volume

9

Issue

2

Start / End Page

449 / 474

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Liu, F., Chakraborty, S., Li, F., Liu, Y., & Lozano, A. C. (2014). Bayesian regularization via graph Laplacian. Bayesian Analysis, 9(2), 449–474. https://doi.org/10.1214/14-BA860
Liu, F., S. Chakraborty, F. Li, Y. Liu, and A. C. Lozano. “Bayesian regularization via graph Laplacian.” Bayesian Analysis 9, no. 2 (January 1, 2014): 449–74. https://doi.org/10.1214/14-BA860.
Liu F, Chakraborty S, Li F, Liu Y, Lozano AC. Bayesian regularization via graph Laplacian. Bayesian Analysis. 2014 Jan 1;9(2):449–74.
Liu, F., et al. “Bayesian regularization via graph Laplacian.” Bayesian Analysis, vol. 9, no. 2, Jan. 2014, pp. 449–74. Scopus, doi:10.1214/14-BA860.
Liu F, Chakraborty S, Li F, Liu Y, Lozano AC. Bayesian regularization via graph Laplacian. Bayesian Analysis. 2014 Jan 1;9(2):449–474.

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

January 1, 2014

Volume

9

Issue

2

Start / End Page

449 / 474

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics