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Rapid Bayesian Inference of Global Network Statistics Using Random Walks.

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Area of Science:

  • Network science
  • Statistical inference
  • Computational mathematics

Background:

  • Analyzing large networks is computationally intensive.
  • Estimating statistical properties often requires exploring a significant portion of the network.
  • Quantifying uncertainty in network analysis is crucial for reliable conclusions.

Purpose of the Study:

  • To develop a rapid and accurate Bayesian methodology for inferring statistical properties of networks.
  • To provide rigorous uncertainty estimates for network parameters.
  • To demonstrate the framework's applicability across various network types and real-world datasets.

Main Methods:

  • Utilizing random walks for efficient network exploration.
  • Applying Bayesian inference to estimate network properties and their probability distributions.
  • Developing a formalism for high-accuracy estimation of node-based properties and network size.

Main Results:

  • High-accuracy estimation of network properties and size with minimal node exploration.
  • Rigorous quantification of parameter uncertainties inherent in the Bayesian approach.
  • Successful demonstration on random, scale-free, and small-world networks, and real-world data like Wikipedia hyperlinks.

Conclusions:

  • The proposed Bayesian random walk methodology offers a computationally efficient and accurate approach to network analysis.
  • This framework provides reliable uncertainty estimates, enhancing the trustworthiness of network property inferences.
  • The method is versatile, applicable to diverse network structures and complex phenomena like epidemic spreading.