Wrapped $\beta$-Gaussians with compact support for exact probabilistic modeling on manifolds

Published: 05 Dec 2023, Last Modified: 05 Dec 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: We introduce wrapped $\beta$-Gaussians, a family of wrapped distributions on Riemannian manifolds, supporting efficient reparametrized sampling, as well as exact density estimation, effortlessly supporting high dimensions and anisotropic scale parameters. We extend Fenchel-Young losses for geometry-aware learning with wrapped $\beta$-Gaussians, and demonstrate the efficacy of our proposed family in a suite of experiments on hypersphere and rotation manifolds: data fitting, hierarchy encoding, generative modeling with variational autoencoders, and multilingual word embedding alignment.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Final version: - add acknowledgments - add a missing citation - fixed typos and minor improvements
Code: https://github.com/ltl-uva/wbg
Supplementary Material: zip
Assigned Action Editor: ~marco_cuturi2
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1351