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Area of Science:

  • Statistical modeling
  • Network analysis
  • Computational statistics

Background:

  • Exponential Random Graph Models (ERGM) are widely used for social network analysis.
  • ERGMs possess intractable likelihood functions, posing significant challenges for posterior sampling.
  • Analyzing large-scale networks with high-dimensional ERGMs remains a computationally intensive problem.

Purpose of the Study:

  • To evaluate the performance of Stochastic Gradient Langevin Dynamics (SGLD) for posterior sampling in ERGMs.
  • To develop a scalable algorithm for analyzing large and complex social networks.
  • To address the long-standing problem of sampling from intractable ERGM likelihoods.

Main Methods:

  • Application of Stochastic Gradient Langevin Dynamics (SGLD), also known as noisy Langevin Monte Carlo.
  • Calculation of stochastic gradients using a short inner Markov chain at each iteration.
  • Theoretical analysis of SGLD convergence properties in the context of growing network sizes.

Main Results:

  • SGLD demonstrates convergence to the true posterior in 2-Wasserstein distance for large network and iteration numbers.
  • Convergence is achieved irrespective of the inner Markov chain length, provided model size grows slowly relative to network size.
  • The proposed SGLD approach offers a scalable solution for high-dimensional ERGM analysis.

Conclusions:

  • SGLD provides an effective and scalable method for analyzing large-scale social networks using ERGMs.
  • The algorithm overcomes the computational hurdles associated with intractable likelihood functions.
  • This research contributes a practical tool for statistical network analysis.