Assessing the credibility of the solutions of incomplete-data inverse problems
Bibliographic record
Abstract
This paper proposes an approach to measure the credibility of solutions of inverse problems with incomplete or missing data, encountered in some physical problems. In such problems, the same set of data can produce multiple solutions, depending on the constraints or assumptions used to compensate for the missing information. The actual “true” solution, against which the quality of a constrained solution can be measured, is not usually available. In this work, we propose to obtain a complete but coarse reference solution that reliably possesses attributes of the actual solution. This is done by solving an over-complete problem with the same set of data but with a coarser structure. A number of residual, composition and fidelity metrics are then used to quantitatively measure the quality of a solution obtained from incomplete data, against the coarse complete reference. The approach was tested with various degrees of incompleteness and different levels of uncertainty (noise) in data in the linear problem of image reconstruction in computed-tomography. The results show that the approach was successful in identifying credible solutions, as well as those that were not trustworthy.
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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 | 0.019 | 0.109 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.006 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".