[2605.00835] Sparse Regression under Correlation and Weak Signals: A Reproducible Benchmark of Classical and Bayesian Methods
Skip to main content
Learn about arXiv becoming an independent nonprofit.
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
> cs > arXiv:2605.00835
Help | Advanced Search
All fields Title Author Abstract Comments Journal reference ACM classification MSC classification Report number arXiv identifier DOI ORCID arXiv author ID Help pages Full text
Search
GO
quick links
Login
Help Pages
About
-->
Computer Science > Machine Learning
arXiv:2605.00835 (cs)
[Submitted on 4 Apr 2026]
Title:Sparse Regression under Correlation and Weak Signals: A Reproducible Benchmark of Classical and Bayesian Methods
Authors:Hao Xiao
View a PDF of the paper titled Sparse Regression under Correlation and Weak Signals: A Reproducible Benchmark of Classical and Bayesian Methods, by Hao Xiao
View PDF HTML (experimental)
Abstract:Choosing between classical and Bayesian sparse regression methods involves a real trade-off: penalized estimators like Lasso run in milliseconds but give no uncertainty estimates,while Horseshoe and Spike-and-Slab priors produce full posteriors but need MCMC chains that take minutes per this http URL few studies compare these two families head-to-head under the conditions that actually make sparse regression hard -- correlated features, weak signals, and growing dimensionality. We benchmark six methods (OLS, Ridge,Lasso, Elastic Net, Horseshoe, Spike-and-Slab) on synthetic data with three covariance structures (rho up to 0.9), four SNR levels, and p in {20, 50, 100}, plus the Diabetes dataset,totalling over 2,600 experiments. The results are clear on some points and nuanced on others. Bayesian methods win on prediction error (MSE 72 vs. 108-267), and the Horseshoe delivers near-nominal 95% coverage (94.8%). But Spike-and-Slab,despite narrower intervals, under-covers at 91.9% -- its continuous relaxation likely plays a role. For variable selection, Lasso and Spike-and-Slab tie at F1 ~ 0.47, making Lasso the practical default when posteriors are not needed. Code and data are available at this https URL.
Comments: 14 pages, 8 figures, 6 tables. Code: this https URL
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2605.00835 [cs.LG]
(or arXiv:2605.00835v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.00835
Focus to learn more
arXiv-issued DOI via DataCite
Submission history
From: Hao Xiao [view email] [v1] Sat, 4 Apr 2026 15:46:44 UTC (71 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Sparse Regression under Correlation and Weak Signals: A Reproducible Benchmark of Classical and Bayesian Methods, by Hao Xiao
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-05
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
export BibTeX citation Loading...
BibTeX formatted citation
×
loading...
Data provided by:
Bookmark
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
About
Help
contact arXivClick here to contact arXiv Contact
subscribe to arXiv mailingsClick here to subscribe Subscribe
Copyright
Privacy Policy
Web Accessibility Assistance
arXiv Operational Status