Related papers: Supervised Training of Conditional Monge Maps
The rapid emergence of single-cell data has facilitated the study of many different biological conditions at the cellular level. Cluster analysis has been widely applied to identify cell types, capturing the essential patterns of the…
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,…
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…
Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to…
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…
Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…
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…
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…
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…
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…
Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan…
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)…
Visual domain adaptation aims to learn discriminative and domain-invariant representation for an unlabeled target domain by leveraging knowledge from a labeled source domain. Partial domain adaptation (PDA) is a general and practical…
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal…
We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…
Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such…
The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…
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…
Monotone gradient functions play a central role in solving the Monge formulation of the optimal transport (OT) problem, which arises in modern applications ranging from fluid dynamics to robot swarm control. When the transport cost is the…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…