An Explicit Description of Extreme Points of the Set of Couplings with Given Marginals: with Application to Minimum-Entropy Coupling Problems

Ya-Jing Ma, Feng Wang, Xian-Yuan Wu +1

Given probability distributions $\mathbf{p}=(p_1,p_2,\dots ,p_m)$ and $\mathbf{q}=(q_1,q_2,\dots ,q_n)$ with $m,n\ge 2$, denote by $\mathcal{C}(\mathbf{p},\mathbf{q})$ the set of all couplings of $\bf…