Structured Matching via Cost-Regularized Unbalanced Optimal Transport

Emanuele Pardini, Katerina Papagiannouli
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2926-2934, 2026.

Abstract

Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data’s underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov–Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov–Wasserstein–type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures (or point clouds) across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-pardini26a, title = { Structured Matching via Cost-Regularized Unbalanced Optimal Transport }, author = {Pardini, Emanuele and Papagiannouli, Katerina}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2926--2934}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/pardini26a/pardini26a.pdf}, url = {https://proceedings.mlr.press/v300/pardini26a.html}, abstract = { Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data’s underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov–Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov–Wasserstein–type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures (or point clouds) across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches. } }
Endnote
%0 Conference Paper %T Structured Matching via Cost-Regularized Unbalanced Optimal Transport %A Emanuele Pardini %A Katerina Papagiannouli %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-pardini26a %I PMLR %P 2926--2934 %U https://proceedings.mlr.press/v300/pardini26a.html %V 300 %X Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data’s underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov–Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov–Wasserstein–type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures (or point clouds) across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches.
APA
Pardini, E. & Papagiannouli, K.. (2026). Structured Matching via Cost-Regularized Unbalanced Optimal Transport . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2926-2934 Available from https://proceedings.mlr.press/v300/pardini26a.html.

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