Related papers: Neural solver for Wasserstein Geodesics and optima…

We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…

In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…

Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…

Recently, Neural Topic Models (NTMs) inspired by variational autoencoders have obtained increasingly research interest due to their promising results on text analysis. However, it is usually hard for existing NTMs to achieve good document…

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness…

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…

The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem…

Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…

Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…

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 novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…

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…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…