arXiv:2606. 17196v1 Announce Type: cross Abstract: This paper is concerned with learning principal variations of random probability measures on $\mathbb{R}^m$ under the Wasserstein geometry.
By Peng Xu, Changbo Zhu, Young-Heon Kim, Xiaohui Chen
arXiv:2411. 15067v2 Announce Type: replace-cross Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space.
By Razvan-Andrei Lascu, Mateusz B. Majka, David \v{S}i\v{s}ka, {\L}ukasz Szpruch
arXiv:2602. 04272v2 Announce Type: replace-cross Abstract: The Importance-Weighted Evidence Lower Bound (IW-ELBO) has emerged as an effective objective for variational inference (VI), tightening the standard ELBO and mitigating the mode-seeking behaviour.
By Peiwen Jiang, Takuo Matsubara, Minh-Ngoc Tran
arXiv:2506. 04480v2 Announce Type: replace-cross Abstract: This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry.
By Nina Vesseron, Elsa Cazelles, Alice Le Brigant, Thierry Klein
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
By Junhyoung Chung, Euijong Song, Won Hwa Kim, Gunwoong Park
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.
By Cl\'ement Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh