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Contour tracking in adverse environments is a challenging problem due to cluttered background, illumination variation, occlusion, and noise, among others. This paper presents a robust contour tracking method by contributing to some of the…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
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…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
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 use of distances based on optimal transportation has recently shown promise for discrimination of power spectra. In particular, spectral estimation methods based on l1 regularization as well as covariance based methods can be shown to…
Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between…
Given a line barrier and a set of mobile sensors distributed in the plane, the Minimizing Maximum Sensor Movement problem (MMSM) for \textcolor{black}{line barrier coverage} is to compute relocation positions for the sensors in the plane…
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…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…
We propose a centralized transportation system that integrates public transit with ridesharing to provide multimodal transportation. At each time interval, the system receives a set of personal drivers, designated drivers, and public…
Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…