Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems
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 vec...
| Authors | Tristan Luca Saidi, Gonzalo Mena, Larry Wasserman et al. |
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| Primary category | stat.ML |
| Published | 24 March 2026 |
| Last updated at source | 24 March 2026 |
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