Jensen-Generalized Discrete Fisher Information, Its Generating Function, and Applications to Image Processing and Contaminated Models
Bibliographic record
Abstract
In this work, we first introduce a discrete version of generalized Fisher information measure and develop some new results for it. We then propose Jensen-generalized discrete Fisher (Jensen-GDF) information as a generalized measure, based on the convexity property of generalized discrete Fisher information measure. We further introduce generating functions for generalized discrete Fisher information and Jensen-GDF information measures and use them to develop some results. We also propose a new correlation coefficient in terms of the generalized discrete Fisher information and discuss some of its properties. Finally, to demonstrate the usefulness of the Jensen-generalized discrete Fisher information measure and the proposed correlation coefficient, we apply them to two real-world examples in image processing and forms of contaminated data, and present corresponding numerical results. Our findings show that the Jensen-GDF information measure and the correlation coefficient introduced here are effective criteria for quantifying similarity between two images in image processing settings and for analyzing contaminated data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".