Related papers: Large-Scale Optimal Transport and Mapping Estimati…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
Many-to-many matching seeks to match multiple points in one set and multiple points in another set, which is a basis for a wide range of data mining problems. It can be naturally recast in the framework of Optimal Transport (OT). However,…
Optimal Mass Transport (OMT) is a well studied problem with a variety of applications in a diverse set of fields ranging from Physics to Computer Vision and in particular Statistics and Data Science. Since the original formulation of Monge…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…
The design of artificial neural networks (ANNs) is inspired by the structure of the human brain, and in turn, ANNs offer a potential means to interpret and understand brain signals. Existing methods primarily align brain signals with…
In the standard formulation of the denoising problem, one is given a probabilistic model relating a latent variable $\Theta \in \Omega \subset \mathbb{R}^m \; (m\ge 1)$ and an observation $Z \in \mathbb{R}^d$ according to: $Z \mid \Theta…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
Unsupervised domain adaptation (UDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain. In this paper, we introduce a novel approach called class-aware optimal transport (OT), which measures the OT…
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…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously,…
Recent years have witnessed a flurry of research activity in graph matching, which aims at finding the correspondence of nodes across two graphs and lies at the heart of many artificial intelligence applications. However, matching…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…
A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
Mixture-of-experts (MoE) models provide a flexible statistical framework for modeling heterogeneity and nonlinear relationships. In many modern applications, however, datasets are naturally distributed across multiple machines due to…