Wrapped Distributions on homogeneous Riemannian manifolds
This work provides a method for modeling data on curved spaces, which is incremental as it builds on existing manifold and distribution theory.
The authors introduced a general framework for constructing probability distributions on Riemannian manifolds using area-preserving maps and isometries, enabling flexible distributions that are easy to sample from and applicable in Monte Carlo algorithms and latent variable models like autoencoders.
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions that are straightforward to sample from, suitable for use within Monte Carlo algorithms and latent variable models, such as autoencoders. As an illustration, we empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model. Finally, we take advantage of the generalized description of this framework to posit questions for future work.