A mixture of experts regression model for functional response with functional covariates
Bibliographic record
Abstract
Abstract Due to the fast growth of data that are measured on a continuous scale, functional data analysis has undergone many developments in recent years. Regression models with a functional response involving functional covariates, also called "function-on-function", are thus becoming very common. Studying this type of model in the presence of heterogeneous data can be particularly useful in various practical situations. We mainly develop in this work a Function-on-Function Mixture of Experts (FFMoE) regression model. Like most of the inference approach for models on functional data, we use basis expansion (B-splines) both for covariates and parameters. A regularized inference approach is also proposed, it accurately smoothes functional parameters in order to provide interpretable estimators. Numerical studies on simulated data illustrate the good performance of FFMoE as compared with competitors. Usefullness of the proposed model is illustrated on two data sets: the reference Canadian weather data set, in which the precipitations are modeled according to the temperature, and a Cycling data set, in which the developed power is explained by the speed, the cyclist heart rate and the slope of the road.
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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 | 0.024 |
| 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 | 0.002 | 0.002 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".