On the sparse Bayesian learning of linear models

Chia Chye Yee and Yves F. Atchadé

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 15, 7672-7691

Abstract: This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting with a sparse signal. We show that in general the SBL estimator does not recover the sparsity structure of the signal. To remedy this, we propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design matrices, the non asymptotic estimation error rate of σslogp/n$\sigma \sqrt{s\log p}/\sqrt{n}$, where n is the sample size, p is the number of regressors, σ is the regression model standard deviation, and s is the number of non zero regression coefficients. We also establish that with high probability the estimator recovers the sparsity structure of the signal. In our simulations we found that the performance of thresholded SBL depends on the strength of the signal. With a weak signal thresholded SBL performs poorly compared to least absolute shrinkage and selection operator (lasso) (Tibshirani, 1996), but outperforms lasso when the signal is strong.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2016.1158837 (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:lstaxx:v:46:y:2017:i:15:p:7672-7691

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2016.1158837

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().