论文标题
使用集线器模型和变体的网络推理的可识别性和一致性
Identifiability and consistency of network inference using the hub model and variants
论文作者
论文摘要
统计网络分析主要集中于推断观察到的网络的参数。在许多应用中，尤其是在社会科学中，观察到的数据是由个别受试者形成的群体。在这些应用程序中，网络本身是统计模型的参数。 Zhao和Weko（2019）提出了一种基于模型的方法，称为HUB模型，以从分组行为中推断出隐式网络。集线器模型假设该组的每个成员都由该组的一个名为中心的成员组合在一起。集线器模型属于Bernoulli混合模型的家族。对于Bernoulli混合物模型而言，参数的可识别性是一个众所周知的困难问题。本文证明了集线器模型参数的可识别性和在轻度条件下的估计一致性。此外，本文通过引入一个模型组件来概括集线器模型，该模型组件允许单个节点自发地出现独立于任何其他个体的模型组。我们将此附加组件称为零组件。新模型弥合了轮毂模型与混合模型的退化情况之间的差距 - 伯努利产品。新模型也证明了可识别性和一致性。提供了数值研究以证明理论结果。
Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko (2019) propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The hub model belongs to the family of Bernoulli mixture models. Identifiability of parameters is a notoriously difficult problem for Bernoulli mixture models. This paper proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this paper generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model -- the Bernoulli product. Identifiability and consistency are also proved for the new model. Numerical studies are provided to demonstrate the theoretical results.
