EP-GIG Priors and Applications in Bayesian Sparse Learning

Zhihua Zhang; Shusen Wang; Dehua Liu; Michael I. Jordan

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arXiv · 1204.4243

EP-GIG Priors and Applications in Bayesian Sparse Learning

Zhihua Zhang·Shusen Wang·Dehua Liu·Michael I. Jordan

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Abstract

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace scale mixtures can subserve a Bayesian framework for sparse learning with nonconvex penalization. The densities of EP-GIG can be explicitly expressed. Moreover, the corresponding posterior distribution also follows a generalized inverse Gaussian distribution. These properties lead us to EM algorithms for Bayesian sparse learning. We show that these algorithms bear an interesting resemblance to iteratively re-weighted $\ell_2$ or $\ell_1$ methods. In addition, we present two extensions for grouped variable selection and logistic regression.

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BibTeX RIS

Zhihua Zhang, Shusen Wang, Dehua Liu, Michael I. Jordan. 2012-04-19. EP-GIG Priors and Applications in Bayesian Sparse Learning. https://arxiv.org/abs/1204.4243

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