arXiv Machine Learning
Sep 17

Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows

The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.

By Francesca Romana Crucinio, Sahani Pathiraja
arXiv Statistics ML
1d ago

Wasserstein-Cram\'er-Rao Theory of Unbiased Estimation

arXiv:2511.07414v2 Announce Type: replace-cross Abstract: The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainmen...

By Nicol\'as Garc\'ia Trillos, Adam Quinn Jaffe, Bodhisattva Sen