A spike-and-slab prior for dimension selection in generalized linear network eigenmodels
本文提出一种基于有序尖峰-平板先验的贝叶斯方法，用于广义线性网络特征模型的维度选择，能处理多种边类型并改进维度估计，在模拟和实际网络数据中表现良好。
Summary Latent space models are often used to model network data by embedding a network’s nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing a class of latent space models we call generalized linear network eigenmodels that can model various edge types (binary, ordinal, nonnegative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. We propose a Bayesian approach to dimension selection for generalized linear network eigenmodels based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. We show that the model’s posterior is consistent and concentrates on low-dimensional models near the truth. We demonstrate our approach’s consistent dimension selection on simulated networks, and we use generalized linear network eigenmodels to study the effect of covariates on the formation of networks from biology, ecology and economics and the existence of residual latent structure.