Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
Gluing methods for quantitative stability of optimal transport maps
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
representative citing papers
Establishes two-mode stability for multi-marginal OT maps with barycentric quadratic cost, yielding 1/4-Hölder estimates for general perturbations and 1/2-Hölder for barycenter-preserving ones, with optimality proofs.
Establishes L^∞-stability of dual potentials in QOT, yielding local Lipschitz stability of the optimal coupling support in Hausdorff distance for quadratic cost under marginal perturbations.
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
Under smooth unit costs and models, empirical subdifferentials of parameterized transport objectives converge graphically almost surely to the population subdifferential, so subgradient methods approach population critical points.
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.
citing papers explorer
-
Near-Lipschitz stability of the Kim--Milman flow map
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
-
Two-mode stability for multi-marginal optimal transport maps
Establishes two-mode stability for multi-marginal OT maps with barycentric quadratic cost, yielding 1/4-Hölder estimates for general perturbations and 1/2-Hölder for barycenter-preserving ones, with optimality proofs.
-
Stability of Quadratically Regularized Optimal Transport
Establishes L^∞-stability of dual potentials in QOT, yielding local Lipschitz stability of the optimal coupling support in Hausdorff distance for quadratic cost under marginal perturbations.
-
Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
-
Statistical Estimation of Monge Transport Maps via Brenier Potentials
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
-
Learning Monge maps with constrained drifting models
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
-
Convergence of empirical subgradients for optimal transport-based objectives
Under smooth unit costs and models, empirical subdifferentials of parameterized transport objectives converge graphically almost surely to the population subdifferential, so subgradient methods approach population critical points.
-
Stability of the Kim--Milman flow map
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.