Related papers: Achieving robustness in classification using optim…

Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…

Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…

Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…

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…

In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…

Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…

Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical…

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…

In this work, we consider the problem of multi-pitch estimation, i.e., identifying super-imposed truncated harmonic series from noisy measurements. We phrase this as recovering a harmonically-structured measure on the unit circle, where the…

We study finite-sample statistical performance guarantees for distributionally robust optimization (DRO) with optimal transport (OT) and OT-regularized divergence model neighborhoods. Specifically, we derive concentration inequalities for…

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

Neural networks are getting better accuracy with higher energy and computational cost. After quantization, the cost can be greatly saved, and the quantized models are more hardware friendly with acceptable accuracy loss. On the other hand,…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

Neural networks are vulnerable to adversarial examples, i.e. inputs that are imperceptibly perturbed from natural data and yet incorrectly classified by the network. Adversarial training, a heuristic form of robust optimization that…

We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while…

In this paper, we present the Lipschitz regularization theory and algorithms for a novel Loss-Sensitive Generative Adversarial Network (LS-GAN). Specifically, it trains a loss function to distinguish between real and fake samples by…

Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be…

Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex…