Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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2026 9representative citing papers
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Gaussian particles in a linearized Bures-Wasserstein space perform consensus optimization for variational inference and outperform deterministic gradient methods on low-dimensional non-log-concave targets.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
SHIELD dataset and distilled DeBERTa v3 model achieve 0.88 micro precision and 0.86 recall on PHI de-identification while matching teacher performance on structured categories.
The paper delivers a chronological history of Fréchet distances connecting early abstract set theory to curve metrics, optimal transport, and the FID metric in generative models.
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