Related papers: On the Complexity of Approximating Multimarginal O…
We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…
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…
Although Sinkhorn divergences are now routinely used in data sciences to compare probability distributions, the computational effort required to compute them remains expensive, growing in general quadratically in the size $n$ of the support…
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.…
Mismatch capacity characterizes the highest information rate for a channel under a prescribed decoding metric, and is thus a highly relevant fundamental performance metric when dealing with many practically important communication…
Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applications, making it robust to data normalization and outliers.…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…
Speculative sampling reduces the latency of autoregressive decoding for target model LLMs without sacrificing inference quality, by using a cheap draft model to suggest a candidate token and a verification criterion to accept or resample…
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…
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to…
Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…
We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
The theory of weak optimal transport (WOT), introduced by [Gozlan et al., 2017], generalizes the classic Monge-Kantorovich framework by allowing the transport cost between one point and the points it is matched with to be nonlinear. In the…
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…