Related papers: Uniform Confidence Band for Optimal Transport Map …
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
Recently, the statistical properties of empirical Entropic Optimal Transport (EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target…
Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. For instance, OT is a popular loss function that quantifies the discrepancy between an…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…
Optimal transport (OT) measures distances between distributions in a way that depends on the geometry of the sample space. In light of recent advances in computational OT, OT distances are widely used as loss functions in machine learning.…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…
We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…
Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…