Optimal subsampling for linear quantile regression models
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Subsampling techniques are efficient methods for handling big data. Quite a few optimal sampling methods have been developed for parametric models in which the loss functions are differentiable with respect to parameters. However, they do not apply to quantile regression (QR) models as the involved check function is not differentiable. To circumvent the non‐differentiability problem, we consider directly estimating the linear QR coefficient by minimizing the Hansen–Hurwitz estimator of the usual loss function for QR. We establish the asymptotic normality of the resulting estimator under a generic sampling method, and then develop optimal subsampling methods for linear QR. In particular, we propose a one‐stage subsampling method, which depends only on the lengths of covariates, and a two‐stage subsampling method, which is a combination of the one‐stage sampling and the ideal optimal subsampling methods. Our simulation and real data based simulation studies show that the two recommended sampling methods always outperform simple random sampling in terms of mean square error, whether the linear QR model is valid or not.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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