Kullback-Leibler distance in linear parametric modeling
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Bibliographic record
Abstract
This paper addresses the estimation of the Kulback-Leibler (KL) distance in data-driven modeling of parametric probability distributions. Given a finite observation of a parametric probability density function (pdf), the goal is to provide the best representative of the true parameter, which is known to belong to a given parametric model set. The first step in this problem setting is to estimate the true parameter in available nested model sets of different orders. The proposed method calculates the KL distance between these estimates and the unknown true parameter. By using only the observed data, we provide probabilistic worst case bounds on these KL distances. The best candidate among the available estimates is the solution of a resulting probabilistic min-max problem. A comparison of this approach with existing methods that estimate the KL distance is provided.
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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 | 0.002 |
| 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