Wrapped $\beta$-Gaussians with Compact Support for Exact Probabilistic Modeling on Manifolds
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.
Cite
Text
Troshin and Niculae. "Wrapped $\beta$-Gaussians with Compact Support for Exact Probabilistic Modeling on Manifolds." Transactions on Machine Learning Research, 2023.Markdown
[Troshin and Niculae. "Wrapped $\beta$-Gaussians with Compact Support for Exact Probabilistic Modeling on Manifolds." Transactions on Machine Learning Research, 2023.](https://mlanthology.org/tmlr/2023/troshin2023tmlr-wrapped/)BibTeX
@article{troshin2023tmlr-wrapped,
title = {{Wrapped $\beta$-Gaussians with Compact Support for Exact Probabilistic Modeling on Manifolds}},
author = {Troshin, Sergey and Niculae, Vlad},
journal = {Transactions on Machine Learning Research},
year = {2023},
url = {https://mlanthology.org/tmlr/2023/troshin2023tmlr-wrapped/}
}