Related papers: Understanding Entropic Regularization in GANs

Classical model-based imaging methods for ultrasound elasticity inverse problem require prior constraints about the underlying elasticity patterns, while finding the appropriate hand-crafted prior for each tissue type is a challenge. In…

Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation,…

We train a generator by maximum likelihood and we also train the same generator architecture by Wasserstein GAN. We then compare the generated samples, exact log-probability densities and approximate Wasserstein distances. We show that an…

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…

As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…

The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Despite its short history, Generative Adversarial Network (GAN) has been extensively studied and used for various tasks, including its original purpose, i.e., synthetic sample generation. However, applying GAN to different data types with…

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training…

One of the main challenges in the parametrization of geological models is the ability to capture complex geological structures often observed in the subsurface. In recent years, generative adversarial networks (GAN) were proposed as an…

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in…

Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized…

This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…

We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport. This framework provides a novel optimal transport distance metric, namely Regularized Wasserstein (RW) discrepancy, which…

High-resolution (HR) precipitation prediction is essential for reducing damage from stationary and localized heavy rainfall; however, HR precipitation forecasts using process-driven numerical weather prediction models remains challenging.…

Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in…

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…

Generative adversarial networks are a class of generative algorithms that have been widely used to produce state-of-the-art samples. In this paper, we investigate GAN to perform anomaly detection on time series dataset. In order to achieve…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…