Nonparametric Methods for Interpretable Copula Calibration and Sparse Functional Classification
Bibliographic record
Abstract
Nonparametric estimation is a novelty statistical method which relaxes the distribution assumption about the relationship between response and covariate, in contrast to parametric estimation. This method has been applied in many field of interest, including density function, regression model and derivative function. One of the important application of nonparametric estimation is modelling dependence among random variables via copula approaches has attracted considerable research attention. With advances in data collection, the strength of dependence often varies according to some covariate, which motivates the dependence calibration using conditional copulas. We propose a penalized estimation framework for the copula parameter function that inherits the flexibility of a nonparametric method and, at the same time, yields a parsimonious and interpretable dependence structure. The theoretical analysis guarantees that the penalized estimators enjoy the oracle properties and behave asymptotically as well as their nonparametric counterparts, while numerical experiments demonstrate the improved empirical performance. We then apply the proposed method to a twin birth weights data. Another important application of nonparametric estimation is classifying the functional data. We consider the classification of sparse functional data that are often encountered in longitudinal studies and other scientific experiments. To utilize the information from not only the functional trajectories but also the observed class labels, we propose a probability enhanced method achieved by weighted support vector machine based on its Fisher consistency property to estimate the effective dimension reduction space. Since only a few measurements are available for some, even all, individuals, a cumulative slicing approach is suggested to borrow information across individuals. We provide justification for validity of the probability-based effective dimension reduction space, and a straightforward implementation that yields a low-dimensional projection space ready for applying standard classifiers. The empirical performance is illustrated through simulated and real examples, particularly in contrast to classication results based on the prominent functional principal component analysis.
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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 | 0.005 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".