Related papers: Optimal Transport Relaxations with Application to …
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect 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…
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…
With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…
Imitation Learning describes the problem of recovering an expert policy from demonstrations. While inverse reinforcement learning approaches are known to be very sample-efficient in terms of expert demonstrations, they usually require…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has two main drawbacks: (i) Wasserstein-1 (or Earth-Mover)…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
We propose moment relaxations for data-driven Wasserstein distributionally robust optimization problems. Conditions are identified to ensure asymptotic consistency of such relaxations for both single-stage and two-stage problems, together…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
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…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss…