相关论文: The Multimarginal Optimal Transport Formulation of…

Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…

Randomization as a mean to improve the adversarial robustness of machine learning models has recently attracted significant attention. Unfortunately, much of the theoretical analysis so far has focused on binary classification, providing…

Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network…

The notion of margin loss has been central to the development and analysis of algorithms for binary classification. To date, however, there remains no consensus as to the analogue of the margin loss for multiclass classification. In this…

In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative…

We revisit the concept of "adversary" in online learning, motivated by solving robust optimization and adversarial training using online learning methods. While one of the classical setups in online learning deals with the "adversarial"…

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…

Deep neural networks, particularly in vision tasks, are notably susceptible to adversarial perturbations. To overcome this challenge, developing a robust classifier is crucial. In light of the recent advancements in the robustness of…

Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…

In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…

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…

In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…

In this work, we propose a new optimization framework for multiclass boosting learning. In the literature, AdaBoost.MO and AdaBoost.ECC are the two successful multiclass boosting algorithms, which can use binary weak learners. We explicitly…

In this paper, mixed categorical structural optimization problems are investigated. The aim is to minimize the weight of a truss structure with respect to cross-section areas, materials and cross-section type. The proposed methodology…

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,…

Adversarial approach has been widely used for data generation in the last few years. However, this approach has not been extensively utilized for classifier training. In this paper, we propose an adversarial framework for classifier…

Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a…

We show that the problem of finding the barycenter in the Hellinger-Kantorovich setting admits a least-cost soft multi-marginal formulation, provided that a one-sided hard marginal constraint is introduced. The constrained approach is then…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…