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Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…

This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…

Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…

In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on…

Asymptotically-optimal motion planners such as RRT* have been shown to incrementally approximate the shortest path between start and goal states. Once an initial solution is found, their performance can be dramatically improved by…

Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…

Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…

Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and…

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 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…

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…

Semantic instance segmentation is the task of simultaneously partitioning an image into distinct segments while associating each pixel with a class label. In commonly used pipelines, segmentation and label assignment are solved separately…

Slicing distribution selection has been used as an effective technique to improve the performance of parameter estimators based on minimizing sliced Wasserstein distance in applications. Previous works either utilize expensive optimization…

We develop a novel method for carrying out model selection for Bayesian autoencoders (BAEs) by means of prior hyper-parameter optimization. Inspired by the common practice of type-II maximum likelihood optimization and its equivalence to…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…