Global optimization for mixed categorical-continuous variables based on Gaussian process models with a randomized categorical space exploration step
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Bibliographic record
Abstract
Real industrial studies often give rise to complex optimization problems involving mixed variables and time consuming simulators. To deal with these difficulties we propose the use of a Gaussian process regression surrogate with a suitable kernel able to capture simultaneously the output correlations with respect to continuous and categorical/discrete inputs without relaxation of the categorical variables. The surrogate is integrated into the Efficient Global Optimization method based on the maximization of the Expected Improvement criterion. This maximization is a Mixed Integer Non-Linear problem which is solved by means of an adequate optimizer: the Mesh Adaptive Direct Search, integrated into the NOMAD library. We introduce a random exploration of the categorical space with a data-based probability distribution and we illustrate the full strategy accuracy on a toy problem. Finally we compare our approach with other optimizers on a benchmark of functions.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.007 |
| 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