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Bayesian hyper-lassos with non-convex penalization

Griffin, Jim E., Brown, Philip J. (2011) Bayesian hyper-lassos with non-convex penalization. Australian and New Zealand Journal of Statistics, 53 (4). pp. 423-442. ISSN 1369-1473. (doi:10.1111/j.1467-842X.2011.00641.x) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:29598)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1111/j.1467-842X.2011.00641.x

Abstract

The Lasso has sparked interest in the use of penalization of the log-likelihood for variable selection, as well as for shrinkage. We are particularly interested in the more-variables-thanobservations case of characteristic importance for modern data. The Bayesian interpretation of the Lasso as the maximum a posteriori estimate of the regression coefficients, which have been given independent, double exponential prior distributions, is adopted. Generalizing this prior provides a family of hyper-Lasso penalty functions, which includes the quasi-Cauchy distribution of Johnstone and Silverman as a special case. The properties of this approach, including the oracle property, are explored, and an EM algorithm for inference in regression problems is described. The posterior is multi-modal, and we suggest a strategy of using a set of perfectly fitting random starting values to explore modes in different regions of the parameter space. Simulations show that our procedure provides significant improvements on a range of established procedures, and we provide an example from chemometrics.

Item Type: Article
DOI/Identification number: 10.1111/j.1467-842X.2011.00641.x
Uncontrolled keywords: Bayesian variable selection; hyper-Lasso; non-convexity; normal-exponential-gamma; oracle property; penalized likelihood
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jim Griffin
Date Deposited: 30 May 2012 12:37 UTC
Last Modified: 16 Nov 2021 10:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/29598 (The current URI for this page, for reference purposes)

University of Kent Author Information

Griffin, Jim E..

Creator's ORCID: https://orcid.org/0000-0002-4828-7368
CReDIT Contributor Roles:

Brown, Philip J..

Creator's ORCID:
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