Related papers: Multiview Sensing With Unknown Permutations: An Op…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…

Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…

The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a…

Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…

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…

Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent…

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…

All-in-one image restoration has emerged as a practical and promising low-level vision task for real-world applications. In this context, the key issue lies in how to deal with different types of degraded images simultaneously. In this…

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…

Motion planning at urban intersections that accounts for the situation context, handles occlusions, and deals with measurement and prediction uncertainty is a major challenge on the way to urban automated driving. In this work, we address…

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…

We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…

We collect some examples of optimal transports in order to explore the (in)stability of the identity map as an optimal transport. First, we consider density and domain perturbations near regular portions of domains. Second, we investigate…

Reliable perception is fundamental for safety critical decision making in autonomous driving. Yet, vision based object detector neural networks remain vulnerable to uncertainty arising from issues such as data bias and distributional…

We present a new approach for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularization on dual Kantorovich potentials. The main bottleneck of…