相关论文: Unbalanced optimal transport for robust longitudin…

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…

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…

Unbalanced optimal transport (UOT) is a natural extension of optimal transport (OT) allowing comparison between measures of different masses. It arises naturally in machine learning by offering a robustness against outliers. The aim of this…

Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…

During training, supervised object detection tries to correctly match the predicted bounding boxes and associated classification scores to the ground truth. This is essential to determine which predictions are to be pushed towards which…

Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such…

Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited. We study unbalanced transport with quadratic cost and…

This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of…

Assessing cancer progression in liver CT scans is a clinical challenge, requiring a comparison of scans at different times for the same patient. Practitioners must identify existing tumors, compare them with prior exams, identify new…

Deep learning-based image restoration methods generally struggle with faithfully preserving the structures of the original image. In this work, we propose a novel Residual-Conditioned Optimal Transport (RCOT) approach, which models image…

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on…

We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…

Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often…

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence…

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…

This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for a class of constrained discrete-time linear systems. UOT compares measures with unequal total mass by balancing…

Survival prediction is a complicated ordinal regression task that aims to predict the ranking risk of death, which generally benefits from the integration of histology and genomic data. Despite the progress in joint learning from pathology…

Joint image registration and segmentation has long been an active area of research in medical imaging. Here, we reformulate this problem in a deep learning setting using adversarial learning. We consider the case in which fixed and moving…

Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applications, making it robust to data normalization and outliers.…

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…