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CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

Cosma Rohilla Shalizi1, Alessandro Rinaldo1

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Summary
This summary is machine-generated.

Many statistical network models fail when applied to sampled data, limiting their usefulness. This study identifies conditions for model consistency and offers solutions for exponential random graph models (ERGMs).

Keywords:
Exponential familyexponential random graph modelindependent incrementsnetwork modelsnetwork samplingprojective familysufficient statistics

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Area of Science:

  • Network Science
  • Statistical Modeling
  • Distributed Systems

Background:

  • Network data is increasingly available, driving interest in statistical models of network structure.
  • Current models often assume consistency under sampling, a property frequently violated by popular exponential random graph models (ERGMs).

Purpose of the Study:

  • To investigate the property of sampling consistency in statistical network models, particularly ERGMs.
  • To demonstrate that many popular ERGMs violate this crucial assumption, limiting their applicability.
  • To provide general results for exponential families of dependent random variables.

Main Methods:

  • Analysis of exponential random graph models (ERGMs) for sampling consistency.
  • Theoretical investigation of exponential families of dependent random variables.
  • Development of conditions for maximum likelihood estimation consistency in ERGMs.

Main Results:

  • Many widely used ERGMs are not consistent under sampling, meaning parameters estimated from sub-networks may not reflect the whole network.
  • Satisfying sampling consistency significantly restricts the expressive power of ERGMs.
  • General conditions for sampling consistency in exponential families were derived.

Conclusions:

  • The assumption of sampling consistency is critical but often overlooked in network modeling.
  • Researchers should carefully check ERGM consistency to ensure valid parameter estimation.
  • The study offers practical guidance for developing and applying statistically sound network models.