Related papers: QC-OT: Optimal Transport with Quasiconformal Mappi…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…
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…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
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…
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…
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…
Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
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…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
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…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
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…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…