Maximum likelihood estimation for reversible mechanistic network models.

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods for instances of graphs generated with mechanistic models, and thus it is near impossible to estimate the parameters using maximum likelihood estimation. In this paper, we propose treating the node sequence in a growing network model as an additional parameter, or as a missing random variable, and maximizing over the resulting likelihood. We develop this framework in the context of a simple mechanistic network model, used to study gene duplication and divergence, and test a variety of algorithms for maximizing the likelihood in simulated graphs. We also run the best-performing algorithm on one human protein-protein interaction network and four nonhuman protein-protein interaction networks. Although we focus on a specific mechanistic network model, the proposed framework is more generally applicable to reversible models.