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Pairwise optimal coupling of multiple random variables

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arxiv 1903.00632 v2 pith:7YWY5U4V submitted 2019-03-02 math.PR math.CO

Omer Angel , Yinon Spinka This is my paper · ORCID
classification math.PRmath.CO
keywords randomvariablescouplingmultipleoptimalpossibleprobabilitythem
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We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between them. In a number of cases we show that the disagreement probability we achieve is the best possible. The proofs of sharpness rely on new results in extremal combinatorics, which may be of independent interest.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pairwise Multi-marginal Optimal Transport and Embedding for Earth Mover's Distance

    math.PR 2019-08 accept novelty 8.0 of 10

    Pairwise multi-marginal optimal transport couplings achieve finite constant-factor ratios only for n=1 or snowflake costs with q<1, with sharp Θ(n^{q/2}) dimension growth on R^n and O(√n log s) distortion on grids.

  2. Fast A/B/n Testing: Exact Multi-Policy Comparison via Tree-Coupled Feedback Sharing

    cs.LG 2026-08 accept novelty 7.0 of 10

    TCAB couples multiple adaptive policies on a tree, shares rewards when their complete context-action pairs match, and preserves each policy's standalone trajectory law at cost T plus cumulative edge disagreement.

  3. Entropy Bounds for Local Coordination and Graph Amenability

    cs.GT 2026-06 unverdicted novelty 7.0 of 10

    Unbiased binary local outputs with average disagreement ε imply the graph is (2h(ε), r)-amenable via mutual-information Shapley measures and grand coupling.

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