Conditional Random Ordered Transport Spaces
A small Wasserstein distance does not certify that a transformation is admissible. In evidence-constrained, semantic, causal, physical, monotone, or risk-sensitive learning, one must ask not only how far two probability laws are, but whether mass has moved in a direction allowed by available information. We introduce conditional random ordered transport spaces (CROTS), a class of \(L^0\)-valued spaces of random probability measures equipped with a Wasserstein ambient metric, a closed stochastic order, hard and soft ordered transport discrepancies, and a conditional risk functional for evaluating order violation under an evidence sigma-field. The central object is an order-admissible trans...
| Authors | Lei Luo, Jian Yang |
|---|---|
| Primary category | cs.LG |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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