论文标题
统一的里曼尼亚歧管上包装的分布
Wrapped Distributions on homogeneous Riemannian manifolds
论文作者
论文摘要
我们提供了一个通用框架，用于利用区域保存图和异构体，以在Riemannian歧管上构建概率分布。控制分布的属性，例如参数，对称性和模态产生一个灵活分布的家族，这些分布是直接从样品中进行样品的一组，适用于蒙特卡洛算法和潜在变量模型，例如自动编码器。作为例证，我们通过在变异自动编码器和潜在空间网络模型中利用我们所提出的分布来验证我们的方法。最后，我们利用对该框架的广义描述为未来的工作提出问题。
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.
