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This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
Recently, Neural Topic Models (NTMs) inspired by variational autoencoders have obtained increasingly research interest due to their promising results on text analysis. However, it is usually hard for existing NTMs to achieve good document…
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…
Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…
Unbalanced optimal transport (UOT) is a natural extension of optimal transport (OT) allowing comparison between measures of different masses. It arises naturally in machine learning by offering a robustness against outliers. The aim of this…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…
This paper concerns the application of techniques from optimal transport (OT) to mean field control, in which the probability measures of interest in OT correspond to empirical distributions associated with a large collection of controlled…
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…
Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a given cost function. In this regard, OT between tractable prior distribution and data has been utilized for generative modeling…
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…
While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
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 (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…