Gibbs posterior for variable selection in high-dimensional classification and data mining

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dc.creatorJiang, Wenxin
dc.creatorTanner, Martin A.
dc.date2008-10-31
dc.date.accessioned2026-07-07T10:14:34Z
dc.date.available2026-07-07T10:14:34Z
dc.descriptionIn the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (such as the classification error) and aims at minimizing a risk function without modeling the data probabilistically. This can improve the performance over the usual Bayesian approach, which depends on a probability model which may be misspecified. Conditions will be provided to achieve good risk performance, even in the presence of high dimensionality, when the number of candidate variables "$K$" can be much larger than the sample size "$n$." In addition, we develop a convenient Markov chain Monte Carlo algorithm to implement BVS with the Gibbs posterior.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS547 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0810.5655
dc.identifierhttp://arxiv.org/abs/0810.5655
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 5, 2207-2231
dc.identifierdoi:10.1214/07-AOS547
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172923
dc.subjectMethodology
dc.subjectMachine Learning
dc.subject62F99 (Primary); 82-08 (Secondary)
dc.titleGibbs posterior for variable selection in high-dimensional classification and data mining
dc.typetext

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