Polynomial Regression Hyperparameter Selection and Analysis using Reconstruction Error Minimization (REM)
Bibliographic record
Abstract
Machine Learning algorithms in Regression modeling generally minimize the mean square error (MSE) of estimation to find the optimum parameters. This MSE, denoted by data error, however, can not be used in hyperparameters selection (HPS) as it is a decreasing function of increasing the dimension of the hyperparameters. Well-known validation methods split the data into training and validation sets for the purpose of HPS. Using the training set for parameter estimation and the validation set for hyperparameter selection. Yet, problem of overestimating (overfitting) in hyperparameter selection causes serious issues in generalizing to unseen data in the learning process. Here we examine the Reconstruction Error Minimization (REM) method of HPS and compare its performance with validation methods. REM-HPS diverges from conventional methods, such as validation and k-fold cross-validation, by utilizing the entire available dataset without the need for splitting it into separate training and validation sets. The whole data is used both in training (parameter selection) and in validation (hyperparameter selection). Simulation results confirm superiority of REM over validation approaches in the sense of accuracy, robustness, and computational complexity. Consequently, it also shows convergence of the approach with smaller data sets. REM results show advantages over validation approaches in the sense of common evaluation metrics such as MSE, R2 (coefficient of determination) and Mean Absolute Percentage Error (MAPE). Unlike validation approaches, REM avoids overfitting. Simulation results provide a comprehensive analysis of the generalizability performance under a range of signal to noise ratio (SNR)s, as data length grows, and for different input data range.
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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 | 0.006 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".