Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds. The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss. The corresponding minimum value is an integrated conditional Fréchet variance, which vanishes exactly ...
| Authors | Kisung You |
|---|---|
| Primary category | stat.ML |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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