Outlier Detection and Robust Estimation in Nonparametric Regression
Why this work is in the frame
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Bibliographic record
Abstract
This paper studies outlier detection and robust estimation for nonparametric regression problems. We propose to include a subject-specific mean shift parameter for each data point such that a nonzero parameter will identify its corresponding data point as an outlier. We adopt a regularization approach by imposing a roughness penalty on the regression function and a shrinkage penalty on the mean shift parameter. An efficient algorithm has been proposed to solve the double penalized regression problem. We discuss a data-driven simultaneous choice of two regularization parameters based on a combination of generalized cross validation and modified Bayesian information criterion. We show that the proposed method can consistently detect the outliers. In addition, we obtain minimax-optimal convergence rates for both the regression function and the mean shift parameter under regularity conditions. The estimation procedure is shown to enjoy the oracle property in the sense that the convergence rates agree with the minimax-optimal rates when the outliers (or regression function) are known in advance. Numerical results demonstrate that the proposed method has desired performance in identifying outliers under different scenarios.
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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 | 0.000 | 0.003 |
| 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