Weak signals in high‐dimensional regression: Detection, estimation and prediction
Bibliographic record
Abstract
Regularization methods, including Lasso, group Lasso and SCAD, typically focus on selecting variables with strong effects while ignoring weak signals. This may result in biased prediction, especially when weak signals outnumber strong signals. This paper aims to incorporate weak signals in variable selection, estimation and prediction. We propose a two-stage procedure, consisting of variable selection and post-selection estimation. The variable selection stage involves a covariance-insured screening for detecting weak signals, while the post-selection estimation stage involves a shrinkage estimator for jointly estimating strong and weak signals selected from the first stage. We term the proposed method as the covariance-insured screening based post-selection shrinkage estimator. We establish asymptotic properties for the proposed method and show, via simulations, that incorporating weak signals can improve estimation and prediction performance. We apply the proposed method to predict the annual gross domestic product (GDP) rates based on various socioeconomic indicators for 82 countries.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.049 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".