Brenier Isotonic Regression

ArXi:2603.10452v1 Announce Type: cross Isotonic regression (IR) is shape-constrained regression to maintain a univariate fitting curve non-decreasing, which has numerous applications including single-index models and probability calibration. When it comes to multi-output regression, the classical IR is no longer applicable because the monotonicity is not readily extendable. We consider a novel multi-output regression problem where a regression function is \emph{cyclically monotone}. Roughly speaking, a cyclically monotone function is the gradient of some convex potential.