Stochastic Blockmodels with Growing Number of Classes

Abstract

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least polylogarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising a collection of Facebook profiles, resulting in block estimates that reveal residual structure.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2011
Accession Number
ADA557851

Entities

People

  • David S. Choi
  • Edoardo Airoldi
  • Patrick J. Wolfe

Organizations

  • Harvard University

Tags

Communities of Interest

  • Biomedical
  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Data Analysis
  • Data Science
  • Information Processing
  • Information Science
  • Military Research
  • Monte Carlo Method
  • Probability
  • Probability Distributions
  • Random Variables
  • Simulations
  • Social Media
  • Social Networking Services
  • Social Networks
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Neural Network Machine Learning.
  • Regression Analysis.
  • Statistical inference.