相关论文: A Vectorial Approach to Unbalanced Optimal Mass Tr…
We examine the optimal mass transport problem in $\mathbb{R}^{n}$ between densities having independent compact support by considering the geometry of a continuous interpolating support boundary in space-time within which the mass density…
Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…
Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…
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…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
We establish quantitative global stability estimates, formulated in terms of optimal transport (OT) cost, for inverse point-source problems governed by elliptic and parabolic equations with spatially varying coefficients. The key idea is…
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…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
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…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
Monolingual word alignment is crucial to model semantic interactions between sentences. In particular, null alignment, a phenomenon in which words have no corresponding counterparts, is pervasive and critical in handling semantically…
Vector-valued Gaussian mixtures form an important special subset of vector-valued distributions. In general, vector-valued distributions constitute natural representations for physical entities, which can mutate or transit among alternative…
The theory of Monge-Kantorovich Optimal Mass Transport (OMT) has in recent years spurred a fast developing phase of research in stochastic control, control of ensemble systems, thermodynamics, data science, and several other fields in…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…
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…
Recent studies have proposed different methods to improve multilingual word representations in contextualized settings including techniques that align between source and target embedding spaces. For contextualized embeddings, alignment…