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- Title
BAYESIAN HYPER-LASSOS WITH NON-CONVEX PENALIZATION.
- Authors
Griffin, Jim E.; Brown, Philip J.
- Abstract
Summary 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-than-observations 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.
- Subjects
BAYESIAN analysis; REGRESSION analysis; ALGORITHMS; CHEMOMETRICS; STATISTICAL decision making
- Publication
Australian & New Zealand Journal of Statistics, 2011, Vol 53, Issue 4, p423
- ISSN
1369-1473
- Publication type
Article
- DOI
10.1111/j.1467-842X.2011.00641.x