相关论文: Understanding Entropic Regularization in GANs

Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the…

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…

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…

The quantization problem aims to find the best possible approximation of probability measures on ${\mathbb{R}}^d$ using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation.…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…

Generative adversarial networks (GANs) are powerful generative models, but usually suffer from instability and generalization problem which may lead to poor generations. Most existing works focus on stabilizing the training of the…

This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…

We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of…

Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…

We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation…

Generative Adversarial Networks (GANs) have become a very popular tool for implicitly learning high-dimensional probability distributions. Several improvements have been made to the original GAN formulation to address some of its…

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…

We use distributionally-robust optimization for machine learning to mitigate the effect of data poisoning attacks. We provide performance guarantees for the trained model on the original data (not including the poison records) by training…

This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of…

Generative Adversial Networks (GANs) have made a major impact in computer vision and machine learning as generative models. Wasserstein GANs (WGANs) brought Optimal Transport (OT) theory into GANs, by minimizing the $1$-Wasserstein distance…

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant…