Open Access
June 2015 Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization
Zhihua Zhang, Jin Li
Bayesian Anal. 10(2): 247-274 (June 2015). DOI: 10.1214/14-BA892


In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete compound Poisson subordinators. We exemplify four specific subordinators: Gamma, Poisson, negative binomial and squared Bessel subordinators. The Laplace exponents of the subordinators are Bernstein functions, so they can be used as sparsity-inducing nonconvex penalty functions. We exploit these subordinators in regression problems, yielding a hierarchical model with multiple regularization parameters. We devise ECME (Expectation/Conditional Maximization Either) algorithms to simultaneously estimate regression coefficients and regularization parameters. The empirical evaluation of simulated data shows that our approach is feasible and effective in high-dimensional data analysis.


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Zhihua Zhang. Jin Li. "Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization." Bayesian Anal. 10 (2) 247 - 274, June 2015.


Published: June 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1335.62073
MathSciNet: MR3420882
Digital Object Identifier: 10.1214/14-BA892

Keywords: Bernstein functions , ECME algorithms , latent shrinkage parameters , nonconvex penalization , Subordinators

Rights: Copyright © 2015 International Society for Bayesian Analysis

Vol.10 • No. 2 • June 2015
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