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 |
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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) |
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