Comparative Analysis of Predictive Performance in Nonparametric Functional Regression: A Case Study of Spectrometric Fat Content Prediction
Bibliographic record
Abstract
Objective: This research aims to compare two nonparametric functional regression models, the Kernel Model and the K-Nearest Neighbor (KNN) Model, with a focus on predicting scalar responses from functional covariates. Two semi-metrics, one based on second derivatives and the other on Functional Principle Component Analysis, are employed for prediction. The study assesses the accuracy of these models by computing Mean Square Errors (MSE) and provides practical applications for illustration. Method: The study delves into the realm of nonparametric functional regression, where the response variable (Y) is scalar, and the covariate variable (x) is a function. The Kernel Model, known as funopare.kernel.cv, and the KNN Model, termed funopare.knn.gcv, are used for prediction. The Kernel Model employs automatic bandwidth selection via Cross-Validation, while the KNN Model employs a global smoothing parameter. The performance of both models is evaluated using MSE, considering two different semi-metrics. Results: The results indicate that the KNN Model outperforms the Kernel Model in terms of prediction accuracy, as supported by the computed MSE. The choice of semi-metric, whether based on second derivatives or Functional Principle Component Analysis, impacts the model's performance. Two real-world applications, Spectrometric Data for predicting fat content and Canadian Weather Station data for predicting precipitation, demonstrate the practicality and utility of the models. Conclusion: This research provides valuable insights into nonparametric functional regression methods for predicting scalar responses from functional covariates. The KNN Model, when compared to the Kernel Model, offers superior predictive performance. The selection of an appropriate semi-metric is essential for model accuracy. Future research may explore the extension of these models to cases involving multivariate responses and consider interactions between response components.
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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 | 0.020 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".