Model selection properties of forward selection and sequential cross‐validation for high‐dimensional regression
Bibliographic record
Abstract
Forward selection (FS) is a popular variable selection method for linear regression. But theoretical understanding of FS with a diverging number of covariates is still limited. We derive sufficient conditions for FS to attain model selection consistency. Our conditions are similar to those for orthogonal matching pursuit, but are obtained using a different argument. When the true model size is unknown, we derive sufficient conditions for model selection consistency of FS with a data‐driven stopping rule, based on a sequential variant of cross‐validation. As a byproduct of our proofs, we also have a sharp (sufficient and almost necessary) condition for model selection consistency of “wrapper” forward search for linear regression. We illustrate intuition and demonstrate performance of our methods using simulation studies and real datasets.
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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 | 0.066 | 0.176 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".