Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures
Why this work is in the frame
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Bibliographic record
Abstract
In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual χ2 divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual χ2 divergence measures. Further, we define Jensen-cumulative residual χ2 (JCR-χ2) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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