Goal Programming Formulations For A Comparative Analysis Of Scalar Norms And Ordinal Vs. Ratio Data
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Bibliographic record
Abstract
Goal programming has proven a valuable mathematical programming form in a number of venues. There has been a similar rapid growth in interest in data mining, where a variety of different data types are encountered. This paper applies goal programming formulations to compare relative performance of L1, L2, and L∞ norms as well as ordinal and ratio data types in a dynamic predictive environment. The models are applied to compare relative accuracy and stability in forecasting a professional athletic environment. Results confirm that ratio data provide more accurate forecasts than ordinal data. Responsiveness to error can be good and bad in prediction. Too much response to outlying events makes the predictor “nervous” and unreliable. L1 metric models are much easier and faster to solve, but involve higher levels of ambiguity than nonlinear models. L1 metric models also were more responsive to changes, but correspondingly tend to be more affected by unexpected outcomes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it