Functional linear quantile regression on a two-dimensional domain
Bibliographic record
Abstract
This article considers the functional linear quantile regression which models the conditional quantile of a scalar response given a functional predictor over a two-dimensional domain. We propose an estimator for the slope function by minimizing the penalized empirical check loss function. Under the framework of reproducing kernel Hilbert space, the minimax rate of convergence for the regularized estimator is established. Using the theory of interpolation spaces on a two- or multi-dimensional domain, we develop a novel result on simultaneous diagonalization of the reproducing and covariance kernels, revealing the interaction of the two kernels in determining the optimal convergence rate of the estimator. Sufficient conditions are provided to show that our analysis applies to many situations, for example, when the covariance kernel is from the Matérn class, and the slope function belongs to a Sobolev space. We implement the interior point method to compute the regularized estimator and illustrate the proposed method by applying it to the hippocampus surface data in the ADNI study.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".