Wasserstein Parallel Transport provides a formal framework for counterfactual prediction in evolving probability distributions.
March 26, 2026
Original Paper
Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems
arXiv · 2603.23736
The Takeaway
This allows researchers to predict how a population (e.g., cells under a drug or a market cohort) would have evolved under different conditions by transporting tangent dynamics along geodesics. It provides the first theoretical guarantees for parallel transport in Wasserstein space, enabling rigorous causal inference for statistical systems.
From the 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 dyn