Related papers: Learning to Generate Wasserstein Barycenters
We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only…
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…
The Wasserstein barycenter (WB) is an important tool for summarizing sets of probability measures. It finds applications in applied probability, clustering, image processing, etc. When the measures' supports are finite, computing a…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in…
We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to…
Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport --…
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges…
This paper considers the problem of measure estimation under the barycentric coding model (BCM), in which an unknown measure is assumed to belong to the set of Wasserstein-2 barycenters of a finite set of known measures. Estimating a…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well…
We develop an estimator-based stochastic fixed-point framework for approximately computing the 2-Wasserstein barycenter of continuous, non-parametric probability measures. Notably, we provide the first rigorous convergence analysis for…
This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
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…
Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…
In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides. The statistical focus is estimating the sample size of measures necessary to calculate an…
Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized…