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

Sergey Troshin, Vlad Niculae

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

Assigned Action Editor: ~marco_cuturi2

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1351