Permuted and Unlinked Monotone Regression in ${\mathbb{R}}^d$: an approach based on mixture modeling and optimal transport

Martin Slawski, Bodhisattva Sen

Suppose that we have a regression problem with response variable Y in ${\mathbb{R}}^d$ and predictor X in ${\mathbb{R}}^d$, for $d\ge 1$. In permuted or unlinked regression we have a…