Development of Adaptive RBF-HDMR Model for Approximating High Dimensional Problems
Why this work is in the frame
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Bibliographic record
Abstract
Modeling or approximating high dimensional, computationally-expensive, black-box problems faces an exponentially increasing difficulty, the “curse-of-dimensionality”. This paper proposes a new form of high-dimensional model representation (HDMR) by integrating the radial basis function (RBF). The developed model, called RBF-HDMR, naturally explores and exploits the linearity/nonlinearity and correlation relationships among variables of the underlying function that is unknown or computationally expensive. This work also derives a lemma that supports the divide-and-conquer and adaptive modeling strategy of RBF-HDMR. RBF-HDMR circumvents or alleviates the “curse-of-dimensionality” by means of its explicit hierarchical structure, adaptive modeling strategy tailored to inherent variable relation, sample reuse, and a divide-and-conquer space-filling sampling algorithm. Multiple mathematical examples of a wide scope of dimensionalities are given to illustrate the modeling principle, procedure, efficiency, and accuracy of RBF-HDMR.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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