Related papers: InfoOT: Information Maximizing Optimal Transport
Domain adaptation aims to transfer knowledge of labeled instances obtained from a source domain to a target domain to fill the gap between the domains. Most domain adaptation methods assume that the source and target domains have the same…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may…
Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this…
Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. This paper applies discrete OT to a swarm of UAVs in a novel way to achieve…
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…