Regularization and Variable Selection via the Elastic Net¶
Zou, H., & Hastie, T. (2005). Regularization and Variable Selection via the Elastic Net. Journal of the Royal Statistical Society Series B: Statistical Methodology, 301-320.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Collinearity Inflation
- Econometric program evaluation — correlated spending measures (per-pupil expenditure, teacher salary, supplies) whose individual coefficients swing across specifications while the joint effect stays stable. Medical and epidemiological modeling — correlated lifestyle covariates (BMI, waist-hip ratio, body fat; sodium and caloric intake) that the model cannot cleanly separate. Marketing-mix and product analytics — correlated channel spend (TV, online video, paid search in the same window) inflating the standard errors on any single channel's ROI. Policy time-series — macro models with overlapping policy instruments and confounded contemporaneous shocks, where the policy coefficient of interest is destabilized. Genomic and high-dimensional regression — correlated SNPs, expression modules, and microbiome OTUs, which is why ridge, lasso, and elastic-net are the standard response
This sourceThe elastic net's grouping behaviour for strongly correlated predictors, motivated by the lasso's unsatisfactory selection under strong correlation.
Supported in partVerified against the publisher's abstract
“the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together”
- Econometric program evaluation — correlated spending measures (per-pupil expenditure, teacher salary, supplies) whose individual coefficients swing across specifications while the joint effect stays stable. Medical and epidemiological modeling — correlated lifestyle covariates (BMI, waist-hip ratio, body fat; sodium and caloric intake) that the model cannot cleanly separate. Marketing-mix and product analytics — correlated channel spend (TV, online video, paid search in the same window) inflating the standard errors on any single channel's ROI. Policy time-series — macro models with overlapping policy instruments and confounded contemporaneous shocks, where the policy coefficient of interest is destabilized. Genomic and high-dimensional regression — correlated SNPs, expression modules, and microbiome OTUs, which is why ridge, lasso, and elastic-net are the standard response
Mechanisms¶
- L1-Regularized Representation Learning
- Its characteristic failure mode is with correlated features: among a group carrying the same signal, L1 tends to keep one almost arbitrarily and zero the rest, so the "chosen" feature is unstable across resamples and the selection reads as more decisive than it is.
This sourceShows that with a group of highly correlated predictors, the lasso tends to select one variable and discard the others without a stable preference among equivalent members of the group.
- Its characteristic failure mode is with correlated features: among a group carrying the same signal, L1 tends to keep one almost arbitrarily and zero the rest, so the "chosen" feature is unstable across resamples and the selection reads as more decisive than it is.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 2 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:42795229a650 · see in the full table