Bibliographic record
Abstract
Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the cost under a nonlinear expectation. This new formulation is motivated by concrete problems in decision theory, robust optimization, and risk management, and it has many distinct features compared with the classic theory. We choose simple cost functions and study different distortion functions and their implications on the optimal transport plan. We show that on the real line, the comonotonic coupling is optimal for the distorted optimal transport problem when the distortion function is convex and the cost function is submodular and monotone. Some forms of duality and uniqueness results are provided. For inverse-S-shaped (SS) distortion functions and linear cost, we obtain the unique form of optimal coupling for all marginal distributions, which turns out to have an interesting “first comonotonic, then countermonotonic” dependence structure; for SS distortion functions, a similar structure is obtained. Our results highlight several challenges and features in distorted optimal transport, offering a new mathematical bridge between the fields of probability, decision theory, and risk management. Funding: R. Wang is supported by the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141 and RGPIN-2024-03728].
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".