论文标题
在潜在位置的两个不同的非可识别性来源上随机图模型
On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models
论文作者
论文摘要
在潜在位置随机图模型的背景下，自然出现了两个独立的非可识别性来源，尽管这两个设置都不是唯一的。在本文中，我们在随机图推理的背景下定义并检查了这两种非身份性，称为子空间的非可见性和基于模型的非识别性。我们举例说明每种类型的非可识别性都在发挥作用，并且在某些设置中，我们如何担心一种或另一种类型的非识别性。然后，我们表征了有或没有子空间的非可识别性的基于模型的非可识别性的限制。我们进一步获得了随机块模型和广义随机点产品图的协方差和$ U $统计量的其他限制结果。
Two separate and distinct sources of nonidentifiability arise naturally in the context of latent position random graph models, though neither are unique to this setting. In this paper we define and examine these two nonidentifiabilities, dubbed subspace nonidentifiability and model-based nonidentifiability, in the context of random graph inference. We give examples where each type of nonidentifiability comes into play, and we show how in certain settings one need worry about one or the other type of nonidentifiability. Then, we characterize the limit for model-based nonidentifiability both with and without subspace nonidentifiability. We further obtain additional limiting results for covariances and $U$-statistics of stochastic block models and generalized random dot product graphs.
