Functional Linear Models with Latent Factors
Bibliographic record
Abstract
We propose a novel functional linear model incorporating latent factors, where scalar response, scalar covariates, and functional covariates have repeated measurements for each subject.Our model accounts for latent factors that may impact the response but remain unobservable.To unveil and estimate these latent factors, we propose an iterated profile estimation method.We then establish the consistency and asymptotic properties of the estimators.To demonstrate the efficacy of our proposed estimation procedure, we conduct simulation studies across various scenarios.We compare our results with estimations derived from conventional functional linear models, revealing the superior performance of our method in addressing latent factors.We further illustrate our proposed model and methodology by analyzing real data from both financial markets and air pollution datasets.In these analyses, we successfully uncover hidden factors that exert influence in these specific fields.
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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 | 0.015 | 0.050 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 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".