Related papers: Wasserstein GANs Work Because They Fail (to Approx…

Modern GANs achieve remarkable performance in terms of generating realistic and diverse samples. This has led many to believe that ``GANs capture the training data manifold''. In this work we show that this interpretation is wrong. We…

We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…

We deconstruct the performance of GANs into three components: 1. Formulation: we propose a perturbation view of the population target of GANs. Building on this interpretation, we show that GANs can be viewed as a generalization of the…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train. The recently proposed Wasserstein GAN (WGAN) creates principled research directions towards addressing these issues. But we found in practice…

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…

We present an estimate of the Wasserstein distance between the data distribution and the generation of score-based generative models. The sampling complexity with respect to dimension is $\mathcal{O}(\sqrt{d})$, with a logarithmic constant.…

Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem…

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…

Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…

Despite the accomplishments of Generative Adversarial Networks (GANs) in modeling data distributions, training them remains a challenging task. A contributing factor to this difficulty is the non-intuitive nature of the GAN loss curves,…

We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…

Many neural-based recommender systems were proposed in recent years and part of them used Generative Adversarial Networks (GAN) to model user-item interactions. However, the exploration of Wasserstein GAN with Gradient Penalty (WGAN-GP) on…

Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…

Obtaining reliable data describing local poverty metrics at a granularity that is informative to policy-makers requires expensive and logistically difficult surveys, particularly in the developing world. Not surprisingly, the poverty…