Related papers: MMD-Regularized Unbalanced Optimal Transport
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.…
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 a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
This paper addresses the problem of estimating entropy-regularized optimal transport (EOT) maps with squared-Euclidean cost between source and target measures that are subGaussian. In the case that the target measure is compactly supported…
Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…
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…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…
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…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…
Maximum Probability Framework, powered by Maximum Probability Theorem, is a recent theoretical development in artificial intelligence, aiming to formally define probabilistic models, guiding development of objective functions, and…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent…