Wrapped Distributions on homogeneous Riemannian manifolds

• URL: http://arxiv.org/abs/2204.09790v1
• Date: Wed, 20 Apr 2022 21:25:21 GMT
• Title: Wrapped Distributions on homogeneous Riemannian manifolds
• Authors: Fernando Galaz-Garcia, Marios Papamichalis, Kathryn Turnbull, Simon Lunagomez, Edoardo Airoldi
• Abstract summary: Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions. We empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model.
• Score: 58.720142291102135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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