Related papers: Optimal Transport with Heterogeneously Missing Dat…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
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…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…
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 unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
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…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…