The half-quadratic approach for high-dimensional robust M-estimation
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we investigate a unified framework, the half-quadratic (HQ) approach, for regularised robust M-estimation. This approach streamlines both numerical and theoretical computations. We introduce augmented objective functions to facilitate robust parameter estimation in both fixed- and high-dimensional settings. These objective functions serve the dual purpose of estimating parameters robustly and detecting influential data points. Specifically, the HQ approach is scrutinised for high-dimensional robust regression, examining the l1- and l2-estimation errors of the proposed regression estimator across various loss functions. Nonasymptotic upper bounds are derived for estimation errors in high-dimensional scenarios. We demonstrate that optimal estimation accuracy can be attained by employing loss functions with bounded derivatives, even in the presence of influential data points. These results remain hold even with heavy-tailed error distributions. Furthermore, the proposed HQ approximation method is compared with existing methods through numerical studies. Additionally, a real dataset is analysed using this proposed methodology.
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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 | 0.001 |
| 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