Related papers: An Optimal Transport Approach for Computing Advers…
Adversarial Training (AT) is one of the most effective methods to train robust Deep Neural Networks (DNNs). However, AT creates an inherent trade-off between clean accuracy and adversarial robustness, which is commonly attributed to the…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
Understanding the fundamental limits of robust supervised learning has emerged as a problem of immense interest, from both practical and theoretical standpoints. In particular, it is critical to determine classifier-agnostic bounds on the…
We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of…
Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal…
Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods such as adversarial training can defend against particular…
Algorithmic trading refers to executing buy and sell orders for specific assets based on automatically identified trading opportunities. Strategies based on reinforcement learning (RL) have demonstrated remarkable capabilities in addressing…
Adversarial training (AT) is a simple yet effective defense against adversarial attacks to image classification systems, which is based on augmenting the training set with attacks that maximize the loss. However, the effectiveness of AT as…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
We theoretically analyse the limits of robustness to test-time adversarial and noisy examples in classification. Our work focuses on deriving bounds which uniformly apply to all classifiers (i.e all measurable functions from features to…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…
While existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real-world settings. In many such cases although test data might not be…
Supervised learning models are challenged by the intrinsic complexities of training data such as outliers and minority subpopulations and intentional attacks at inference time with adversarial samples. While traditional robust learning…
The rise of computer vision applications in the real world puts the security of the deep neural networks at risk. Recent works demonstrate that convolutional neural networks are susceptible to adversarial examples - where the input images…
Despite their overwhelming success on a wide range of applications, convolutional neural networks (CNNs) are widely recognized to be vulnerable to adversarial examples. This intriguing phenomenon led to a competition between adversarial…
We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the agnostic-classifier setting. We prove the existence of Borel…
Machine learning-based forecasting models are commonly used in Intelligent Transportation Systems (ITS) to predict traffic patterns and provide city-wide services. However, most of the existing models are susceptible to adversarial attacks,…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…