相关论文: LCOT: Linear circular optimal transport

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…

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,…

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…

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…

Optimal transport (OT) is a popular measure to compare probability distributions. However, OT suffers a few drawbacks such as (i) a high complexity for computation, (ii) indefiniteness which limits its applicability to kernel machines. In…

Preference learning in Large Language Models (LLMs) has advanced significantly, yet existing methods remain limited by modest performance gains, high computational costs, hyperparameter sensitivity, and insufficient modeling of global…

This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of…

We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…

Although vital to computer vision systems, few-shot action recognition is still not mature despite the wide research of few-shot image classification. Popular few-shot learning algorithms extract a transferable embedding from seen classes…

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 (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…

Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…

Entropic optimal transport (EOT) presents an effective and computationally viable alternative to unregularized optimal transport (OT), offering diverse applications for large-scale data analysis. In this work, we derive novel statistical…

Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…

We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…

Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One…

Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…

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…

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…

Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes $n$ and $m$ in $\mathbb{R}^d$, entropic OT (EOT)…