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Fast Computation of Free-Support Wasserstein Medians

stat.CO · 2026-06-17 · unverdicted · novelty 7.0

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.

Primitive Sequences for Probability Measures on Compact Intervals

math.PR · 2026-05-08 · unverdicted · novelty 7.0

Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.

A homogenization principle for total variation

math.PR · 2026-04-04 · conditional · novelty 7.0

Total variation between products of measures is at least a universal constant times that between the averaged measures' products.

A parameterized family of balance indices for phylogenetic networks

math.CO · 2026-06-23 · unverdicted · novelty 6.0

Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.

Scale selection for geometric medians on product manifolds

math.ST · 2026-05-08 · unverdicted · novelty 6.0

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.

Density Evolution: A Multiscale View of Density Estimation

math.ST · 2026-05-29 · unverdicted · novelty 5.0

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.

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