Spectral Inference for Large Stochastic Blockmodels with Nodal Covariates

61 Pages Posted: 21 Aug 2019 Last revised: 14 Feb 2022

See all articles by Angelo Mele

Angelo Mele

Johns Hopkins University - Carey Business School

Lingxin Hao

Johns Hopkins University

Joshua Cape

Independent

Carey Priebe

Johns Hopkins University

Date Written: August 18, 2019

Abstract

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. We show that a network model with discrete unobserved link heterogeneity and binary (or discrete) covariates corresponds to a stochastic blockmodel (SBM). We develop a spectral estimator for the effect of covariates on link probabilities, exploiting the correspondence of SBMs and generalized random dot product graphs (GRDPG). 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. Finally, we establish asymptotic normality of our estimators.

Keywords: conditionally independent links, stochastic blockmodel, spectral estimation, generalized random dot product graphs, large networks, asymptotic normality

Suggested Citation

Mele, Angelo and Hao, Lingxin and Cape, Joshua and Priebe, Carey, Spectral Inference for Large Stochastic Blockmodels with Nodal Covariates (August 18, 2019). Available at SSRN: https://ssrn.com/abstract=3438987 or http://dx.doi.org/10.2139/ssrn.3438987

Angelo Mele (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

HOME PAGE: http://www.meleangelo.com

Lingxin Hao

Johns Hopkins University ( email )

Baltimore, MD 21218
United States
(410) 516-4022 (Phone)
(410) 516-7590 (Fax)

Joshua Cape

Independent ( email )

Carey Priebe

Johns Hopkins University ( email )

Dept. of Mathematical Sciences
Baltimore, MD 21218
United States
410-516-7198 (Phone)
410-516-7459 (Fax)

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