A fast parameter estimator for large complex networks

Abstract

Abstract Many natural phenomena are the results of interactions of different components. For example, an organism’s phenotype results from interactions of genes, proteins and the environment. The characteristics of our society are shaped by how people relate to each other. The internet is the product of billions of interconnected computers, electronic devices and users. To understand systems, we represent them using networks, that is, random graphs. A critical inferential step is to estimate the parameters of these networks. Often analytical likelihood estimators for random graph parameters are unknown. In these cases, non-parametric approximations for likelihood estimators can be used. However, known non-parametric estimators for complex network models are computationally inefficient. Here, we present a linear time and space non-parametric estimator for massive networks ($\mathcal{O}(n)$). We show that our method precisely estimates the parameters of networks composed of five million nodes in a few hours. In contrast, a usual approach would need 900 years.