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.

中文翻译：

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齐次黎曼流形上的环绕分布

我们提供了一个通用框架，用于在黎曼流形上构建概率分布，利用区域保留图和等距图。对分布属性（例如参数、对称性和模态）的控制会产生一系列灵活的分布，这些分布可以直接从中采样，适用于 Monte Carlo 算法和潜在变量模型（例如自动编码器）。作为说明，我们通过在变分自动编码器和潜在空间网络模型中利用我们提出的分布来经验验证我们的方法。最后，我们利用这个框架的概括描述来为未来的工作提出问题。