Related papers: Scalable Optimal Transport Methods in Machine Lear…
In past work on fairness in machine learning, the focus has been on forcing the prediction of classifiers to have similar statistical properties for people of different demographics. To reduce the violation of these properties, fairness…
Network topology has significant impacts on operational performance of power systems. While extensive research efforts have been devoted to optimization of network topology for improving various system performances, the problem of how to…
We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…
Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applications, making it robust to data normalization and outliers.…
Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the…
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from…
Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
The orienteering problem (OP) is a combinatorial optimization problem that seeks a path visiting a subset of locations to maximize collected rewards under a limited resource budget. This article presents a systematic PRISMA-based review of…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
With the advent of large datasets, offline reinforcement learning (RL) is a promising framework for learning good decision-making policies without the need to interact with the real environment. However, offline RL requires the dataset to…
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…
Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…
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…
Training data are usually limited or heterogeneous in many chemical and biological applications. Existing machine learning models for chemistry and materials science fail to consider generalizing beyond training domains. In this article, we…
Out-of-distribution (OOD) detection is crucial for ensuring the reliability and safety of machine learning models in real-world applications. While zero-shot OOD detection, which requires no training on in-distribution (ID) data, has become…
Optimal transport (OT) theory describes general principles to define and select, among many possible choices, the most efficient way to map a probability measure onto another. That theory has been mostly used to estimate, given a pair of…