Related papers: On the Existence of Optimal Transport Gradient for…

In scene graph generation (SGG), learning with cross-entropy loss yields biased predictions owing to the severe imbalance in the distribution of the relationship labels in the dataset. Thus, this study proposes a method to generate scene…

In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…

We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…

The practical realization of end-to-end training of communication systems is fundamentally limited by its accessibility of the channel gradient. To overcome this major burden, the idea of generative adversarial networks (GANs) that learn to…

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

Generative Adversarial Networks (GANs) are commonly used for modeling complex distributions of data. Both the generators and discriminators of GANs are often modeled by neural networks, posing a non-transparent optimization problem which is…

Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train.…

Generative adversarial networks (GANs) are a recently proposed class of generative models in which a generator is trained to optimize a cost function that is being simultaneously learned by a discriminator. While the idea of learning cost…

In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…

In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and…

In this paper, we study the problem of learning compact (low-dimensional) representations for sequential data that captures its implicit spatio-temporal cues. To maximize extraction of such informative cues from the data, we set the problem…

Although Sinkhorn divergences are now routinely used in data sciences to compare probability distributions, the computational effort required to compute them remains expensive, growing in general quadratically in the size $n$ of the support…

We have developed a new data-driven paradigm for the rapid inference, modeling and simulation of the physics of transport phenomena by deep learning. Using conditional generative adversarial networks (cGAN), we train models for the direct…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…

Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…

Generative adversarial networks have been very successful in generative modeling, however they remain relatively challenging to train compared to standard deep neural networks. In this paper, we propose new visualization techniques for the…

This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…