Bibliographic record
Abstract
We consider the problem of estimating an unknown convex function f_* (0, 1)^d →R from data (X1, Y1), … (X_n; Y_n).A simple approach is finding a convex function that is the closest to the data points by minimizing the sum of squared errors over all convex functions. The convex regression estimator, which is computed this way, su ers from a drawback of having extremely large subgradients near the boundary of its domain. To remedy this situation, the penalized convex regression estimator, which minimizes the sum of squared errors plus the sum of squared norms of the subgradient over all convex functions, is recently proposed. In this paper, we prove that the penalized convex regression estimator and its subgradient converge with probability one to f_* and its subgradient, respectively, as n → ∞, and hence, establish the legitimacy of the penalized convex regression estimator.  
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".