Related papers: Outlier-Robust Optimal Transport: Duality, Structu…

Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…

Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…

Deep neural networks achieve superior performance in semantic segmentation, but are limited to a predefined set of classes, which leads to failures when they encounter unknown objects in open-world scenarios. Recognizing and segmenting…

Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…

Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…

The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT…

We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem…

Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…

We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several…

We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…

Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive…