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Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
Computing the empirical Wasserstein distance in the Wasserstein-distance-based independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
\textbf{Motivation:} Predicting single-cell perturbation responses requires mapping between two unpaired single-cell data distributions. Optimal transport (OT) theory provides a principled framework for constructing such mappings by…
Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…
This paper studies a combined space partitioning and network flow optimization problem, with applications to large-scale power, transportation, or communication systems. In dense wireless networks, one may want to simultaneously optimize…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
Optimal transport (OT) theory describes general principles to define and select, among many possible choices, the most efficient way to map a probability measure onto another. That theory has been mostly used to estimate, given a pair of…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…