Designing Ambiguity Sets for Distributionally Robust Optimization Using Structural Causal Optimal Transport
Bibliographic record
Abstract
Distributionally robust optimization tackles out-of-sample issues like overfitting and distribution shifts by adopting an adversarial approach over a range of possible data distributions, known as the ambiguity set. To balance conservatism and accuracy, these sets must include realistic probability distributions by leveraging information from the nominal distribution. Assuming that nominal distributions arise from a structural causal model with a directed acyclic graph G and structural equations, previous methods such as adapted and G-causal optimal transport have only utilized causal graph information in designing ambiguity sets. In this work, we propose incorporating structural equations, which include causal graph information, to enhance ambiguity sets, resulting in more realistic distributions. We introduce structural causal optimal transport and its associated ambiguity set, demonstrating their advantages and connections to previous methods. A key benefit of our approach is a relaxed version, where a regularization term replaces the complex causal constraints, enabling an efficient algorithm via difference-of-convex programming to solve structural causal optimal transport. We also show that when structural information is absent and must be estimated, our approach remains effective and provides finite sample guarantees. Lastly, we address the radius of ambiguity sets, illustrating how our method overcomes the curse of dimensionality in optimal transport problems, achieving faster shrinkage with dimension-free order.
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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 | 0.007 | 0.025 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".