Estimation of Multivariate Smooth Functions via Convex Programs
Bibliographic record
Abstract
A new method for estimating an unknown, multivariate function from noisy data is proposed in the case where the unknown function is assumed to be smooth. The proposed method finds the minimizer of the smoothness of a function while imposing an upper bound on the sum of squared errors between the function and the data set. The proposed estimator is designed to be numerically sound by eliminating the dependency on any artificially plugged-in parameters that traditional methods use and by tackling the ill-conditioned numerical settings that traditional methods suffer from. Hence, it is expected to perform better than existing estimators numerically. We prove the existence of the proposed estimator and show that we can compute the proposed estimator through a convex program. Empirical studies illustrate that the proposed method is effectively applied to the problem of estimating the average payoff of a stock option that is contingent on two different stocks.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".