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THEORY-1210: When several networks are aligned, fitting one joint multi-marginal coupling finds held-out correspondences better than fitting them in pairs, and the gain comes from the joint fit itself, not from the cost or the search space that come with it

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Properties4
StatusProposed
Tagsnetwork-science, mathematics
SourceLIT-1814 — Hierarchical Multi-Marginal Optimal Transport for Network Alignment
ExtendsTHEORY-1159 — Aligning three networks jointly, through one multi-marginal fused Gromov–Wasserstein coupling with an anchor-based random-walk cost and a cluster decomposition, finds held-out correspondences better than pairwise and existing multi-network methods in most cases, as the paper's plots show, in both pairwise and whole-tuple hits, on benchmarks whose true correspondences are consistent across the three networks by construction; whether the joint coupling itself is the cause is not separated from the new cost and the clustering

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Source

Zeng et al. (2024), LIT-1814, §5 (pp. 5–7) of arXiv 2310.04470v2; read in full in NOTE-1334. What the experiments showed is THEORY-1159, which this entry extends; the identity behind joint fitting is THEORY-1132.

The thesis

The paper attributes HOT’s larger margins on high-order hits to aligning the networks jointly rather than in pairs (p. 5). If that is right, joint fitting is a useful regularizer wherever the true correspondences are transitive.

Why it is not held

HOT changed three things at once: the random-walk-with-restart cost from shared anchors, the cluster decomposition, and the joint coupling. No ablation holds the first two fixed while changing the third, and on attributed DBLP the plain version does nearly as well, which the paper credits to the cost (p. 13). Every benchmark’s truth is a consistent set of triples, so the comparison cannot show whether consistency costs true local distinctions where the truth is not transitive (QUESTION-319).

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