Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation.
This article advocates proximal Markov chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of th...
| Publicado en: | American Statistician Vol. 78; no. 4; pp. 379 - 391 |
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| Autores principales: | , , , |
| Formato: | Artículo |
| Publicado: |
Taylor & Francis Ltd
Nov2024
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=180359691&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 180359691 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Nov2024 vid: 78 iid: 4 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 180359691 10.1080/00031305.2024.2308821 ppf: 379 ppct: 12 formats: tig: atl: Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation. aug: au: Zhou, Xinkai Heng, Qiang Chi, Eric C. Zhou, Hua affil: Department of Biostatistics, UCLA, Los Angeles, CA Department of Computational Medicine, UCLA, Los Angeles, CA Department of Statistics, Rice University, Houston, TX su: Markov chain Monte Carlo Bayesian field theory Inferential statistics Machine learning Parameter estimation Regularization parameter sug: subj: Markov chain Monte Carlo Bayesian field theory Inferential statistics Machine learning Parameter estimation Regularization parameter keyword: Hamiltonian Monte Carlo Moreau-Yosida envelope Proximal mapping Hamiltonian Monte Carlo Moreau-Yosida envelope Proximal mapping ab: This article advocates proximal Markov chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of the total-variation regularization term, fixes variance and regularization strength parameters as constants, and uses the Langevin algorithm for the posterior sampling. We extend ProxMCMC to be fully Bayesian by providing data-adaptive estimation of all parameters including the regularization strength parameter. More powerful sampling algorithms such as Hamiltonian Monte Carlo are employed to scale ProxMCMC to high-dimensional problems. Analogous to the proximal algorithms in optimization, ProxMCMC offers a versatile and modularized procedure for conducting statistical inference on constrained and regularized problems. The power of ProxMCMC is illustrated on various statistical estimation and machine learning tasks, the inference of which is traditionally considered difficult from both frequentist and Bayesian perspectives. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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