Related papers: Training Wasserstein GANs without gradient penalti…
Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal…
In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional…
To improve the stability of GAN training we need to understand why they can produce realistic samples. Presently, this is attributed to properties of the divergence obtained under an optimal discriminator. This argument has a fundamental…
Generative Adversarial Networks (GANs) are the most popular image generation models that have achieved remarkable progress on various computer vision tasks. However, training instability is still one of the open problems for all GAN-based…
This paper introduces a novel approach to image denoising that leverages the advantages of Generative Adversarial Networks (GANs). Specifically, we propose a model that combines elements of the Pix2Pix model and the Wasserstein GAN (WGAN)…
Generative Adversarial Networks (GANs) are one of the most popular tools for learning complex high dimensional distributions. However, generalization properties of GANs have not been well understood. In this paper, we analyze the…
Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dimensional distributions, but training them is considered hard. A possible explanation for training instabilities is the inherent imbalance…
Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
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 present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…
Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
Optimizing the discriminator in Generative Adversarial Networks (GANs) to completion in the inner training loop is computationally prohibitive, and on finite datasets would result in overfitting. To address this, a common update strategy is…
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
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…
In this paper, we propose a new adversarial training framework to address high-dimensional instantaneous channel estimation in wireless communications. Specifically, we train a generative adversarial network to predict a channel realization…
We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…