Variance estimation in high-dimensional linear regression via adaptive elastic-net
Bibliographic record
Abstract
Variance estimation in high-dimensional linear regression is a fundamental problem in statistical learning, and it plays a wide range of roles in signal processing, pattern recognition, and other fields. Because it is difficult to choose the true model precisely in high-dimensional regression, variance estimation remains a challenging problem, especially in scenarios where the true regression parameter has a large number of non-zero elements. In this paper, we develop a novel approach for variance estimation by solving a re-parameterized log-likelihood optimization problem with adaptive elastic-net regularization. It is called the natural adaptive elastic-net (NAEN). The relationship between NAEN and the naive adaptive elastic-net is established. The NAEN inherits the advantages of the naive adaptive elastic-net, that is, it can select and estimate the regression and variance parameters simultaneously. Moreover, we also give the asymptotic properties of NAEN for error variance. The simulation results show that the proposed NAEN is suitable for scenarios where the true regression parameter has many non-zero elements.
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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 | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".