An Orthogonal Matching Pursuit Variable Screening Algorithm for High-Dimensional Linear Regression Models
Why this work is in the frame
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Bibliographic record
Abstract
Variable selection plays an important role in data mining. It is crucial to filter useful variables and extract useful information in a high-dimensional setup when the number of predictor variables <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>d</a:mi> </a:math> tends to be much larger than the sample size <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>n</c:mi> </c:math> . Statistical inferences can be more precise after irrelevant variables are moved out by the screening method. This article proposes an orthogonal matching pursuit algorithm for variable screening under the high-dimensional setup. The proposed orthogonal matching pursuit method demonstrates good performance in variable screening. In particular, if the dimension of the true model is finite, OMP might discover all relevant predictors within a finite number of steps. Throughout theoretical analysis and simulations, it is confirmed that the orthogonal matching pursuit algorithm can identify relevant predictors to ensure screening consistency in variable selection. Given the sure screening property, the BIC criterion can be used to practically select the best candidate from the models generated by the OMP algorithm. Compared with the traditional orthogonal matching pursuit method, the resulting model can improve prediction accuracy and reduce computational cost by screening out the relevant variables.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it