arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
By Sre\'cko {\DJ}ura\v{s}inovi\'c, Jean-Bernard Lasserre, Victor Magron
arXiv:2606. 00413v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response.
By Thibault Pautrel, Fran\c{c}ois Portier
Principal Component Analysis (PCA) is a fundamental tool for statistical dimension reduction, yet no canonical extension to distribution-valued data has emerged within the framework of optimal transpo...
The paper introduces LOT Wassmap, an algorithm designed to uncover low‑dimensional structures in the Wasserstein space without computing a full pairwise distance matrix. It leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to accelerate computations, and provides theoretical guarantees on embedding quality even when only finite samples are available. Experiments show that LOT Wassmap achieves accurate embeddings that improve with larger sample sizes while significantly reducing computational cost compared to traditional pairwise‑distance‑based methods.
By Alexander Cloninger, Keaton Hamm, Varun Khurana, Caroline Moosm\"uller
The paper introduces Lifted PCA, a canonical extension of Euclidean PCA to the Wasserstein space of probability measures. By lifting variational formulations on the Stiefel and Grassmann manifolds, the authors derive equivalent minimization problems over probability measures that correspond to Wasserstein barycenters with generalized costs. The work establishes dual formulations, optimality conditions, connections to multimarginal optimal transport, statistical consistency, and computational algorithms, and demonstrates practical performance on distributional datasets.
By J\'er\'emie Bigot, Cl\'ement Bonet
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon