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Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…
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…
Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational…
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…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
The Unbalanced Optimal Transport (UOT) problem plays increasingly important roles in computational biology, computational imaging and deep learning. Scaling algorithm is widely used to solve UOT due to its convenience and good convergence…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…
Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models as even subtle changes could incur significant performance drops. Being able to estimate a model's performance on test data is important in practice…
We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…