Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization

Zhihua Zhang; Jin Li

doi:10.1214/14-ba892

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arXiv · 1308.6069

Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization

Zhihua Zhang·Jin Li

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Abstract

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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BibTeX RIS

Zhihua Zhang, Jin Li. 2015-05-15. Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization. https://doi.org/10.1214/14-ba892

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