# Spectral inference for large Stochastic Blockmodels with nodal covariates

## TL;DR

This paper introduces spectral estimators for unobserved community structures and covariate effects in large stochastic blockmodels, providing faster computation and asymptotic inference capabilities, with applications to social network data.

## Contribution

It develops a novel spectral estimation method for both unobserved blocks and covariate effects, with proven asymptotic normality and improved computational efficiency over existing algorithms.

## Key findings

- Estimator performs well across different data scenarios.
- Application reveals homophily and unobserved communities in Facebook data.
- Method scales efficiently for large networks.

## Abstract

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of covariates in stochastic blockmodels. On the theoretical side, we establish asymptotic normality of our estimators for the subsequent purpose of performing inference. On the applied side, we show that computing our estimator is much faster than standard variational expectation--maximization algorithms and scales well for large networks. Monte Carlo experiments suggest that the estimator performs well under different data generating processes. Our application to Facebook data shows evidence of homophily in gender, role and campus-residence, while allowing us to discover unobserved communities. The results in this paper provide a foundation for spectral estimation of the effect of observed covariates as well as unobserved latent community structure on the probability of link formation in networks.