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Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models
Daniel Bartl, Stephan Eckstein
https://arxiv.org/abs/2510.09270 https://…

Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models
Using i.i.d. data to estimate a high-dimensional distribution in Wasserstein distance is a fundamental instance of the curse of dimensionality. We explore how structural knowledge about the data-generating process which gives rise to the distribution can be used to overcome this curse. More precisely, we work with the set of distributions of probabilistic graphical models for a known directed acyclic graph. It turns out that this knowledge is only helpful if it can be quantified, which we forma…

Differentially Private Wasserstein Barycenters
Anming Gu, Sasidhar Kunapuli, Mark Bun, Edward Chien, Kristjan Greenewald
https://arxiv.org/abs/2510.03021 https://

Differentially Private Wasserstein Barycenters
The Wasserstein barycenter is defined as the mean of a set of probability measures under the optimal transport metric, and has numerous applications spanning machine learning, statistics, and computer graphics. In practice these input measures are empirical distributions built from sensitive datasets, motivating a differentially private (DP) treatment. We present, to our knowledge, the first algorithms for computing Wasserstein barycenters under differential privacy. Empirically, on synthetic d…

Desiderata for a biomedical knowledge network: opportunities, challenges and future Directions
Chunlei Wu, Hongfang Liu, Jason Flannick, Mark A. Musen, Andrew I. Su, Lawrence Hunter, Thomas M. Powers, Cathy H. Wu
https://arxiv.org/abs/2509.22424

Desiderata for a biomedical knowledge network: opportunities, challenges and future Directions
Knowledge graphs, collectively as a knowledge network, have become critical tools for knowledge discovery in computable and explainable knowledge systems. Due to the semantic and structural complexities of biomedical data, these knowledge graphs need to enable dynamic reasoning over large evolving graphs and support fit-for-purpose abstraction, while establishing standards, preserving provenance and enforcing policy constraints for actionable discovery. A recent meeting of leading scientists di…