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Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…

统计理论 · 数学 2026-04-08 François Bachoc , Alberto González-Sanz , Jean-Michel Loubes , Yisha Yao

Algorithmic stability is an important notion that has proven powerful for deriving generalization bounds for practical algorithms. The last decade has witnessed an increasing number of stability bounds for different algorithms applied on…

机器学习 · 统计学 2023-10-31 Lingjiong Zhu , Mert Gurbuzbalaban , Anant Raj , Umut Simsekli

We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with…

统计理论 · 数学 2020-11-09 Moritz Haas , Stefan Richter

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…

机器学习 · 计算机科学 2021-02-16 Yifei Wang , Peng Chen , Wuchen Li

Machine learning models are vulnerable to Adversarial Examples: minor perturbations to input samples intended to deliberately cause misclassification. Current defenses against adversarial examples, especially for Deep Neural Networks (DNN),…

密码学与安全 · 计算机科学 2019-01-04 Kathrin Grosse , David Pfaff , Michael Thomas Smith , Michael Backes

Design of adversarial attacks for deep neural networks, as well as methods of adversarial training against them, are subject of intense research. In this paper, we propose methods to train against distributional attack threats, extending…

机器学习 · 计算机科学 2025-02-14 Xingjian Bai , Guangyi He , Yifan Jiang , Jan Obloj

Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…

机器学习 · 计算机科学 2025-02-04 Wenqian Li , Yan Pang

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation…

计算机视觉与模式识别 · 计算机科学 2019-09-09 Vinay Kyatham , Mayank Mishra , Tarun Kumar Yadav , Deepak Mishra , Prathosh AP

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…

大气与海洋物理 · 物理学 2020-11-16 Gabriele Vissio , Valerio Lembo , Valerio Lucarini , Michael Ghil

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

统计方法学 · 统计学 2022-02-14 Ryo Okano , Masaaki Imaizumi

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…

机器学习 · 统计学 2017-10-23 Nicolas Courty , Rémi Flamary , Mélanie Ducoffe

We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification,…

机器学习 · 计算机科学 2021-11-05 Nam Ho-Nguyen , Stephen J. Wright

Projected Gradient Descent (PGD) is a strong and widely used first-order adversarial attack, yet its computational cost scales poorly, as all training samples undergo identical iterative inner-loop optimization despite contributing…

机器学习 · 计算机科学 2025-12-29 Youran Ye , Dejin Wang , Ajinkya Bhandare

This paper describes a new approach for training generative adversarial networks (GAN) to understand the detailed 3D shape of objects. While GANs have been used in this domain previously, they are notoriously hard to train, especially for…

计算机视觉与模式识别 · 计算机科学 2017-11-01 Edward Smith , David Meger

Generating high-quality and interpretable adversarial examples in the text domain is a much more daunting task than it is in the image domain. This is due partly to the discrete nature of text, partly to the problem of ensuring that the…

机器学习 · 计算机科学 2019-05-31 Samuel Barham , Soheil Feizi

The generative adversarial imitation learning (GAIL) has provided an adversarial learning framework for imitating expert policy from demonstrations in high-dimensional continuous tasks. However, almost all GAIL and its extensions only…

机器学习 · 计算机科学 2020-12-09 Ming Zhang , Yawei Wang , Xiaoteng Ma , Li Xia , Jun Yang , Zhiheng Li , Xiu Li

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…

数值分析 · 数学 2022-08-10 Yihang Gao , Michael K. Ng

Generative Adversarial Networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player…

机器学习 · 统计学 2021-09-14 Yao Chen , Qingyi Gao , Xiao Wang

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

计算机视觉与模式识别 · 计算机科学 2019-04-16 Jiqing Wu , Zhiwu Huang , Dinesh Acharya , Wen Li , Janine Thoma , Danda Pani Paudel , Luc Van Gool

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

计算机视觉与模式识别 · 计算机科学 2019-04-17 Jiqing Wu , Zhiwu Huang , Dinesh Acharya , Wen Li , Janine Thoma , Danda Pani Paudel , Luc Van Gool