论文标题
主要流动
Principal Manifold Flows
论文作者
论文摘要
归一化的流量使用双线转化将一组独立的潜在变量映射到其样品中。尽管样本和潜在变量之间的确切对应关系，但它们的高水平关系尚未得到很好的了解。在本文中，我们使用主歧管表征流的几何结构，并使用轮廓来了解潜在变量和样品之间的关系。我们介绍了一种新颖的归一化流量，称为主歧管流（PF），其轮廓是其主要歧管，并且是注射流（IPF）的变体，它比常规注射式流动更有效地训练。 PF可以使用任何流程结构构建，以正则最大似然的目标进行训练，并可以对其所有主要歧管进行密度估计。在我们的实验中，我们表明PFS和IPF能够在各种数据集上学习主要歧管。此外，我们表明，PFS可以对位于具有可变维度的多种歧管上的数据进行密度估计，而现有的归一化流量是不可能的。
Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In this paper we characterize the geometric structure of flows using principal manifolds and understand the relationship between latent variables and samples using contours. We introduce a novel class of normalizing flows, called principal manifold flows (PF), whose contours are its principal manifolds, and a variant for injective flows (iPF) that is more efficient to train than regular injective flows. PFs can be constructed using any flow architecture, are trained with a regularized maximum likelihood objective and can perform density estimation on all of their principal manifolds. In our experiments we show that PFs and iPFs are able to learn the principal manifolds over a variety of datasets. Additionally, we show that PFs can perform density estimation on data that lie on a manifold with variable dimensionality, which is not possible with existing normalizing flows.
