Related papers: Optimal Transport driven CycleGAN for Unsupervised…
For a given image generation problem, the intrinsic image manifold is often low dimensional. We use the intuition that it is much better to train the GAN generator by minimizing the distributional distance between real and generated images…
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…
Optimal transport (OT) offers a versatile framework to compare complex data distributions in a geometrically meaningful way. Traditional methods for computing the Wasserstein distance and geodesic between probability measures require…
We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric space. Our method is based on an unbalanced optimal transport…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
Unpaired image-to-image translation has broad applications in art, design, and scientific simulations. One early breakthrough was CycleGAN that emphasizes one-to-one mappings between two unpaired image domains via generative-adversarial…
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the…
Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, $\mu$ and $\nu$, which is useful in many applications. Available algorithms for computing these maps do not appear to…
Generative adversarial networks (GANs) have shown great success in applications such as image generation and inpainting. However, they typically require large datasets, which are often not available, especially in the context of prediction…
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)…
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…
Generative adversarial network (GAN) has been shown to be useful in various applications, such as image recognition, text processing and scientific computing, due its strong ability to learn complex data distributions. In this study, a…
Generative models based on latent variables, such as generative adversarial networks (GANs) and variational auto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields. However, many data such as…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…
Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…
The Generative Adversarial Networks (GAN) framework is a well-established paradigm for probability matching and realistic sample generation. While recent attention has been devoted to studying the theoretical properties of such models, a…
Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…