Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood.

Area of Science:

• Computational Social Science
• Bioinformatics
• Network Science

Background:

• Network models are crucial in social and genome sciences for understanding relational data.
• Latent space models offer interpretable spatial representations but suffer from O(N^2) computational cost, limiting scalability.
• Existing methods are often infeasible for analyzing large-scale networks.

Purpose of the Study:

• To develop a computationally efficient approximation for latent space models.
• To enable the analysis of large networks that were previously intractable.
• To improve the identification of false positive links in biological networks.

Main Methods:

• Proposed an approximation of the log-likelihood function for latent space models.
• Adapted the case-control methodology from epidemiology to construct an unbiased case-control likelihood estimator.
• Integrated the case-control likelihood into Markov Chain Monte Carlo (MCMC) estimation, reducing computational complexity from O(N^2) to O(N).

Main Results:

• The case-control likelihood approximation significantly reduces computational time, making latent space models scalable to large networks.
• Evaluated performance using both simulated and real-world datasets, demonstrating the method's validity.
• Successfully applied the model to a large protein-protein interaction network.

Conclusions:

• The case-control likelihood provides a computationally efficient and scalable alternative for latent space model estimation.
• This method facilitates the analysis of large networks and aids in identifying false positive links, particularly in biological contexts.
• The approach enhances the practical applicability of latent space models across various scientific domains.