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Tag: transport

  • Learning Paths for Dynamic Measure Transport: A Control Perspective

    Learning Paths for Dynamic Measure Transport: A Control Perspective arXiv:2511.03797v1 Announce Type: new Abstract: We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for learning alternate…

  • Simplifying Optimal Transport through Schatten-$p$ Regularization

    Simplifying Optimal Transport through Schatten-$p$ Regularization arXiv:2510.11910v1 Announce Type: new Abstract: We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional…

  • What is a good matching of probability measures? A counterfactual lens on transport maps

    What is a good matching of probability measures? A counterfactual lens on transport maps arXiv:2509.16027v1 Announce Type: new Abstract: Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are not identifiable:…

  • Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks

    Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks arXiv:2508.10888v1 Announce Type: new Abstract: The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of point clouds or networks.…

  • Optimal Transport with Heterogeneously Missing Data

    Optimal Transport with Heterogeneously Missing Data arXiv:2505.17291v1 Announce Type: new Abstract: We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous missingness probabilities across features and across the two distributions.…

  • Optimal Transport-Based Domain Adaptation for Rotated Linear Regression

    Optimal Transport-Based Domain Adaptation for Rotated Linear Regression arXiv:2505.09229v1 Announce Type: new Abstract: Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target domain for improved model transfer, we focus…

  • Optimal Transport for Machine Learners

    Optimal Transport for Machine Learners arXiv:2505.06589v1 Announce Type: new Abstract: Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important tool in machine learning, especially for designing and evaluating generative models. These course notes cover…

  • Optimal Scheduling of Dynamic Transport

    Optimal Scheduling of Dynamic Transport arXiv:2504.14425v1 Announce Type: new Abstract: Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this…