[2603.23736] Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems

Statistics > Machine Learning arXiv:2603.23736 (stat) [Submitted on 24 Mar 2026] Title:Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems Authors:Tristan Luca Saidi, Gonzalo Mena, Larry Wasserman, Florian Gunsilius View a PDF of the paper titled Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems, by Tristan Luca Saidi and 3 other authors View PDF HTML (experimental) Abstract:Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial conditions is fundamental to causal inference, domain adaptation, and counterfactual prediction. However, the space of distributions often lacks the vector space structure on which classical methods rely. To address this, we introduce a general notion of parallel dynamics at a distributional level. We base this principle on parallel transport of tangent dynamics along optimal transport geodesics and call it ``Wasserstein Parallel Trends''. By replacing the vector subtraction of classic methods with geodesic parallel transport, we can provide counterfactual comparisons of distributional dynamics in applications such as causal inference, domain adaptation, and batch-effect correction in experimental settings. The main mathematical contribution is a novel notion of fanning scheme on the Wasserstein manifold that all...