We provide the first information theoretic tight analysis for inference of
latent community structure given a sparse graph along with high dimensional
node covariates, correlated with the same latent communities. Our work bridges
recent theoretical breakthroughs in the detection of latent community structure
without nodes covariates and a large body of empirical work using diverse
heuristics for combining node covariates with graphs for inference. The
tightness of our analysis implies in particular, the information theoretical
necessity of combining the different sources of information. Our analysis holds
for networks of large degrees as well as for a Gaussian version of the model.

本文提供了第一个信息理论的紧密分析，以推断与相同潜在社区相关的高维节点协变量的稀疏图中的潜在社区结构。

情境随机块模型

Contextual Stochastic Block Models

Biological and social systems consist of myriad interacting units. The
interactions can be represented in the form of a graph or network. Measurements
of these graphs can reveal the underlying structure of these interactions,
which provides insight into the systems that generated the graphs. Moreover, in
applications such as connectomics, social networks, and genomics, graph data
are accompanied by contextualizing measures on each node. We utilize these node
covariates to help uncover latent communities in a graph, using a modification
of spectral clustering. Statistical guarantees are provided under a joint
mixture model that we call the node-contextualized stochastic blockmodel,
including a bound on the mis-clustering rate. The bound is used to derive
conditions for achieving perfect clustering. For most simulated cases,
covariate-assisted spectral clustering yields results superior to regularized
spectral clustering without node covariates and to an adaptation of canonical
correlation analysis. We apply our clustering method to large brain graphs
derived from diffusion MRI data, using the node locations or neurological
region membership as covariates. In both cases, covariate-assisted spectral
clustering yields clusters that are easier to interpret neurologically.

通过改进的谱聚类方法，利用节点协变量帮助揭示图中的潜在社区，该方法综合考虑了节点上的上下文信息，应用于在大脑扩散 MRI 数据中的大脑图研究中，得到了更易于在神经学上进行解释的社区聚类效果。