Defines the L² over Wasserstein space to equip random probability measures with inherited Riemannian geometry, enabling statistical convergence results and Bayesian posterior consistency in the Wasserstein topology.
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Introduces the MCB estimator for pointwise Wasserstein barycenter quantile estimation under sparse sampling by modeling the distribution of latent unit-level quantiles via marginal CDF distributions estimated with binomial mixtures, with consistency and asymptotic normality.
DeSI estimates a single index via deep neural network for conditional Fréchet mean regression in metric spaces, with claimed uniform approximation, convergence rates, and empirical performance on distributions, networks, SPD matrices, and mood data.
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$L^2$ over Wasserstein: Statistical Analysis for Optimal Transport
Defines the L² over Wasserstein space to equip random probability measures with inherited Riemannian geometry, enabling statistical convergence results and Bayesian posterior consistency in the Wasserstein topology.