Related papers: Local Bures-Wasserstein Transport: A Practical and…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…
Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…
Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…
This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables…
A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the…
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
The optimal transport and Wasserstein barycenter of Gaussian distributions have been solved. In literature, the closed form formulas of the Monge map, the Wasserstein distance and the Wasserstein barycenter have been given. Moreover, when…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT…
Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically…
Let $R$ and $B$ be two point sets in $\mathbb{R}^d$, with $|R|+ |B| = n$ and where $d$ is a constant. Next, let $\lambda : R \cup B \to \mathbb{N}$ such that $\sum_{r \in R } \lambda(r) = \sum_{b \in B} \lambda(b)$ be demand functions over…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…