Related papers: Relaxed Wasserstein with Applications to GANs

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the…

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…

This paper presents a novel feature selection method leveraging the Wasserstein distance to improve feature selection in machine learning. Unlike traditional methods based on correlation or Kullback-Leibler (KL) divergence, our approach…

Projecting the distance measures onto a low-dimensional space is an efficient way of mitigating the curse of dimensionality in the classical Wasserstein distance using optimal transport. The obtained maximized distance is referred to as…

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound…

Non-saturating generative adversarial network (GAN) training is widely used and has continued to obtain groundbreaking results. However so far this approach has lacked strong theoretical justification, in contrast to alternatives such as…

Recent advancements in real image editing have been attributed to the exploration of Generative Adversarial Networks (GANs) latent space. However, the main challenge of this procedure is GAN inversion, which aims to map the image to the…

The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…

Magnetic Resonance Imaging (MRI) is a crucial imaging modality for viewing internal body structures. This research work analyses the performance of popular GAN models for accurate and precise MRI reconstruction by enhancing image quality…

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…

Unsupervised learning of disentangled representations involves uncovering of different factors of variations that contribute to the data generation process. Total correlation penalization has been a key component in recent methods towards…

Learning based single image super resolution (SISR) task is well investigated in 2D images. However, SISR for 3D Magnetics Resonance Images (MRI) is more challenging compared to 2D, mainly due to the increased number of neural network…

Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an…

The $2$-Wasserstein distance is sensitive to minor geometric differences between distributions, making it a very powerful dissimilarity metric. However, due to this sensitivity, a small outlier mass can also cause a significant increase in…

Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…

In federated learning, participating clients typically possess non-i.i.d. data, posing a significant challenge to generalization to unseen distributions. To address this, we propose a Wasserstein distributionally robust optimization scheme…

Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein…

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…