Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation

Xinkai Zhou, Qiang Heng, Eric C. Chi and Hua Zhou

The American Statistician, 2024, vol. 78, issue 4, 379-390

Abstract: 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.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2024.2308821 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:amstat:v:78:y:2024:i:4:p:379-390

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20

DOI: 10.1080/00031305.2024.2308821

Access Statistics for this article

The American Statistician is currently edited by Eric Sampson

More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().