Scalable Approximate Bayesian Computation for Growing Network Models via Extrapolated and Sampled Summaries.

Area of Science:

• Computational Statistics
• Network Science
• Statistical Inference

Background:

• Approximate Bayesian computation (ABC) is a powerful simulation-based, likelihood-free inference method.
• ABC is computationally intensive, especially for large datasets and complex models like growing networks.
• Existing ABC methods struggle with the scale and computational demands of mechanistic network growth models.

Purpose of the Study:

• To develop novel methodological approaches for enabling Approximate Bayesian computation (ABC) in large growing network models.
• To enhance the computational efficiency of ABC for parameter estimation and model selection in network science.
• To address the limitations of traditional ABC methods when dealing with large-scale, incrementally generated data.

Main Methods:

• Proposed a procedure to extrapolate summary statistics from small to large networks using least squares and Gaussian processes.
• Introduced the use of sample-based summary statistics instead of census-based ones to reduce computational cost.
• Applied these methods to mechanistic models of network growth.

Main Results:

• The developed methods significantly reduce the computational burden of ABC for large growing networks.
• The resulting ABC posterior distribution closely approximates the posterior from standard, computationally expensive ABC methods.
• Extrapolated and sampled summary statistics proved effective for inference in large network models.

Conclusions:

• The proposed methodological advancements make ABC a more feasible and efficient tool for inferring parameters in large, growing network models.
• These techniques of summary statistic extrapolation and sampling offer broader applicability to other incremental data generation scenarios in ABC.
• The study bridges a gap in statistical inference tools for complex network models.