{"ID":2837540,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19075","arxiv_id":"2511.19075","title":"Structured Matching via Cost-Regularized Unbalanced Optimal Transport","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.","short_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,...","url_abs":"https://arxiv.org/abs/2511.19075","url_pdf":"https://arxiv.org/pdf/2511.19075v2","authors":"[\"Emanuele Pardini\",\"Katerina Papagiannouli\"]","published":"2025-11-24T13:11:27Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.AP\"]","methods":"[]","has_code":false}