Maximum likelihood estimation for mechanistic network models

TL;DR

This paper introduces a novel likelihood estimation framework for mechanistic network models by treating node sequences as missing data, enabling parameter inference in complex network growth models.

Contribution

It proposes a new approach to estimate parameters in mechanistic network models by maximizing likelihood over node sequences, applicable to reversible models.

Findings

Developed algorithms for likelihood maximization in simulated graphs

Applied the method to human and non-human protein-protein interaction networks

Demonstrated the framework's general applicability to reversible models

Abstract

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 because of a combinatorial explosion in outcomes of repeated applications of the mechanism. Thus it is near impossible to estimate the parameters using maximum likelihood estimation. In this paper, we propose treating 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 a human protein-protein interaction network and four non-human protein-protein interaction networks. Although we focus on a specific mechanistic network model here, the proposed framework is more generally applicable to reversible models.