Penalized function-on-function partial leastsquares regression
Bibliographic record
Abstract
This paper deals with the "function-on-function'" or "fully functional" linear regression problem. We address the problem by proposing a novel penalized Function-on-Function Partial Least-Squares (pFFPLS) approach that imposes smoothness on the PLS weights. Our proposal introduces an appropriate finite-dimensional functional space with an associated set of bases on which to represent the data and controls smoothness with a roughness penalty operator. Penalizing the PLS weights imposes smoothness on the resulting coefficient function, improving its interpretability. In a simulation study, we demonstrate the advantages of pFFPLS compared to non-penalized FFPLS. Our comparisons indicate a higher accuracy of pFFPLS when predicting the response and estimating the true coefficient function from which the data were generated. We also illustrate the advantages of our proposal with two case studies involving two well-known datasets from the functional data analysis literature. In the first one, we predict log precipitation curves from the yearly temperature profiles recorded in 35 weather stations in Canada. In the second case study, we predict the hip angle profiles during a gait cycle of children from their corresponding knee angle profiles.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".