Related papers: On the Wasserstein alignment problem
We perform a mathematical and statistical analysis of the Wasserstein least squares problem, a regression method for vector-valued covariates and distribution-valued responses. Our proposal contrasts with other distributional regression…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
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…
Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…
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 transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach -- we search for mutually…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of…
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…
Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…
We develop a theory for image restoration with a learned regularizer that is analogous to that of Meyer's characterization of solutions of the classical variational method of Rudin-Osher-Fatemi (ROF). The learned regularizer we use is a…
Wasserstein Generative Adversarial Networks (WGANs) are the popular generative models built on the theory of Optimal Transport (OT) and the Kantorovich duality. Despite the success of WGANs, it is still unclear how well the underlying OT…
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…