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The subject of this paper is the estimation of a probability measure on ${\mathbb R}^d$ from data observed with an additive noise, under the Wasserstein metric of order $p$ (with $p\geq 1$). We assume that the distribution of the errors is…

Statistics Theory · Mathematics 2013-07-22 Jérôme Dedecker , Bertrand Michel

Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax…

Statistics Theory · Mathematics 2021-01-21 Zheng Liu , Po-Ling Loh

Deep-learning-based NLP models are found to be vulnerable to word substitution perturbations. Before they are widely adopted, the fundamental issues of robustness need to be addressed. Along this line, we propose a formal framework to…

Computation and Language · Computer Science 2022-01-12 Yuting Yang , Pei Huang , FeiFei Ma , Juan Cao , Meishan Zhang , Jian Zhang , Jintao Li

In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an…

Machine Learning · Computer Science 2021-10-01 Abed AlRahman Al Makdah , Vaibhav Katewa , Fabio Pasqualetti

We propose a novel deterministic purification method to improve adversarial robustness by mapping a potentially adversarial sample toward a nearby sample that lies close to a mode of the data distribution, where classifiers are more…

Machine Learning · Computer Science 2026-02-09 Vinh Hoang , Sebastian Krumscheid , Holger Rauhut , Raúl Tempone

Modern machine learning models with very high accuracy have been shown to be vulnerable to small, adversarially chosen perturbations of the input. Given black-box access to a high-accuracy classifier $f$, we show how to construct a new…

Machine Learning · Computer Science 2019-12-17 Grzegorz Głuch , Rüdiger Urbanke

We show that label noise exists in adversarial training. Such label noise is due to the mismatch between the true label distribution of adversarial examples and the label inherited from clean examples - the true label distribution is…

Machine Learning · Computer Science 2023-10-17 Chengyu Dong , Liyuan Liu , Jingbo Shang

We study Label-Smoothing as a means for improving adversarial robustness of supervised deep-learning models. After establishing a thorough and unified framework, we propose several variations to this general method: adversarial, Boltzmann…

Machine Learning · Computer Science 2019-10-16 Morgane Goibert , Elvis Dohmatob

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…

Machine Learning · Computer Science 2020-01-30 Farhad Farokhi

Most machine learning classifiers, including deep neural networks, are vulnerable to adversarial examples. Such inputs are typically generated by adding small but purposeful modifications that lead to incorrect outputs while imperceptible…

Machine Learning · Computer Science 2017-09-28 Beilun Wang , Ji Gao , Yanjun Qi

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…

Machine Learning · Computer Science 2023-01-03 Tianyi Lin , Chenyou Fan , Nhat Ho , Marco Cuturi , Michael I. Jordan

In a reinforcement learning (RL) setting, the agent's optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent's ability to make…

Machine Learning · Computer Science 2025-09-23 Anthony Coache , Sebastian Jaimungal

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…

Computation and Language · Computer Science 2019-11-12 Georgios Balikas , Ioannis Partalas

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Optimization and Control · Mathematics 2019-05-27 Emilie Chouzenoux , Henri Gérard , Jean-Christophe Pesquet

Machine-learning architectures, such as Convolutional Neural Networks (CNNs) are vulnerable to adversarial attacks: inputs crafted carefully to force the system output to a wrong label. Since machine-learning is being deployed in…

Cryptography and Security · Computer Science 2022-11-03 Amira Guesmi , Ihsen Alouani , Khaled N. Khasawneh , Mouna Baklouti , Tarek Frikha , Mohamed Abid , Nael Abu-Ghazaleh

Randomized smoothing has become a leading method for achieving certified robustness in deep classifiers against l_{p}-norm adversarial perturbations. Current approaches for achieving certified robustness, such as data augmentation with…

Machine Learning · Computer Science 2024-05-28 Jieren Deng , Hanbin Hong , Aaron Palmer , Xin Zhou , Jinbo Bi , Kaleel Mahmood , Yuan Hong , Derek Aguiar

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the…

Machine Learning · Computer Science 2016-03-30 Alhussein Fawzi , Omar Fawzi , Pascal Frossard

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…

Computer Vision and Pattern Recognition · Computer Science 2018-12-04 Lijun Zhang , Yujin Zhang , Yongbin Gao

Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time. In this work we highlight the benefits of natural low rank representations that often exist for real data…

Machine Learning · Computer Science 2020-08-04 Pranjal Awasthi , Himanshu Jain , Ankit Singh Rawat , Aravindan Vijayaraghavan

To collect large scale annotated data, it is inevitable to introduce label noise, i.e., incorrect class labels. To be robust against label noise, many successful methods rely on the noisy classifiers (i.e., models trained on the noisy…

Computer Vision and Pattern Recognition · Computer Science 2020-11-23 Songzhu Zheng , Pengxiang Wu , Aman Goswami , Mayank Goswami , Dimitris Metaxas , Chao Chen