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The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
We study the problem of designing hard negative sampling distributions for unsupervised contrastive representation learning. We propose and analyze a novel min-max framework that seeks a representation which minimizes the maximum…
Recently, the statistical properties of empirical Entropic Optimal Transport (EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational…
This paper concerns the application of techniques from optimal transport (OT) to mean field control, in which the probability measures of interest in OT correspond to empirical distributions associated with a large collection of controlled…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…