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LIT-1806: Causal Optimal Transport of Abstractions

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Properties5
StatusActive — read in full 2026-10-29 (NOTE-1342) from arXiv v1; worth reading as the first method to learn a causal abstraction map from paired interventional samples without the structural equations, and for what it shows unintentionally: its do-calculus term is constant on the feasible set as written, so its gains come from an intervention-compatibility cost.
Version2
Tagscausality, mathematics
Cited as “paper” byNOTE-1342 — Felekis et al. — Causal optimal transport of abstractions
Cited as “source” byTHEORY-1123 — In COTA's formulation of causal abstraction learning as multi-marginal optimal transport, the term meant to impose do-calculus relations between the transport plans of comparable interventions depends only on the plans' marginals and on normalisers built from them, which the transport constraints fix to the empirical distributions, so it is constant on the feasible set; its weight changes the solution only by rescaling the cost and entropy weights, and the paper's evidence that the constraints help, a sweep over that weight, cannot separate the two, THEORY-1137 — When an abstraction map between two causal models is learned by optimal transport from paired interventional distributions, a transport cost that rewards pairs of states compatible with the same paired interventions gives much lower held-out abstraction error than a Hamming cost when the intervention set is rich, and higher error when it holds only a few, because with few interventions the compatibility cost is nearly uniform

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Felekis, Y., Zennaro, F. M., Branchini, N., & Damoulas, T. (2024). Causal optimal transport of abstractions. CLeaR 2024, PMLR 236, 462–498.

Why this is here

A7’s bridge between pragmatic transport and distributed agency: a correspondence that respects interventions, not only observations, so that systems matched on relational statistics but different under perturbation are told apart (CLAIM-414, CASE-179, THEORY-849). A good abstraction still does not settle constitution (CLAIM-150).

The reading (NOTE-1342) corrects this in part. COTA does fit every paired interventional distribution, not only the observational one, so a held-out intervention can expose a bad map. But it assumes the two models are related and learns a map; it does not tell systems apart. Its target notion is Rubenstein et al.’s one-distribution exact transformation, relaxed and made stochastic, which is weaker than THEORY-849’s reading of causal abstraction and open to CLAIM-399’s objection. And its do-calculus term, the part said to carry the causal structure, is inert as written (THEORY-1123).

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