{A Finite-Sample Generalization Bound for Semiparametric Regression: Partially Linear Models}
Bibliographic record
Abstract
In this paper we provide generalization bounds for semiparametric regression with the so-called partially linear models where the regression function is written as the sum of a linear parametric and a nonlinear, non-parametric function, the latter taken from a some set H with finite entropy-integral. The problem is technically challenging because the parametric part is unconstrained and the model is underdetermined, while the response is allowed to be unbounded with subgaussian tails. Under natural regularity conditions, we bound the generalization error as a function of the metric entropy of H and the dimen-sion of the linear model. Our main tool is a ratio-type concentration inequality for incre-ments of empirical processes, based on which we are able to give an exponential tail bound on the size of the parametric component. We also provide a comparison to alternatives of this technique and discuss why and when the unconstrained parametric part in the model may cause a problem in terms of the expected risk. We also explain by means of a specific example why this problem cannot be detected using the results of classical asymptotic anal-ysis often seen in the statistics literature. 1
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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 | 0.026 | 0.093 |
| Meta-epidemiology (narrow) | 0.004 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.005 | 0.008 |
| Research integrity | 0.004 | 0.011 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".