论文标题
里曼尼亚人连续归一化流
Riemannian Continuous Normalizing Flows
论文作者
论文摘要
归一化的流量显示了以计算障碍方式对柔性概率分布进行建模的巨大希望。但是，尽管数据通常是在诸如球体，托里和双曲线空间之类的riemannian歧管上自然描述的，但最归一化的流量隐含地假设了平坦的几何形状，使它们在这些情况下弄清楚或不合适。为了克服这个问题，我们介绍了Riemannian连续归一化流，该模型通过将流量定义为普通微分方程的解决方案，该模型接受了光滑歧管上灵活概率测量的参数化。我们表明，与标准流量或先前引入的投影流相比，这种方法可以导致合成和现实数据的实质性改进。
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic spaces, most normalizing flows implicitly assume a flat geometry, making them either misspecified or ill-suited in these situations. To overcome this problem, we introduce Riemannian continuous normalizing flows, a model which admits the parametrization of flexible probability measures on smooth manifolds by defining flows as the solution to ordinary differential equations. We show that this approach can lead to substantial improvements on both synthetic and real-world data when compared to standard flows or previously introduced projected flows.
