Maximum likelihood: extracting unbiased information from complex networks

TL;DR

This paper demonstrates that the Maximum Likelihood principle provides a rigorous method for unbiased parameter estimation in complex network models, enabling the extraction of hidden variables from topological data.

Contribution

It introduces a framework for unbiased network models based on ML, addressing biases and enabling hidden variable inference from topology.

Findings

ML yields unique, statistically rigorous parameters.

Biased models are inherently ill-defined when ML conditions are unmet.

Recovered GDP from network topology in World Trade Web data.

Abstract

The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the Maximum Likelihood (ML) principle indicates a unique, statistically rigorous parameter choice, associated to a well defined topological feature. We then find that, if the ML condition is incompatible with the built-in parameter choice, network models turn out to be intrinsically ill-defined or biased. To overcome this problem, we construct a class of safely unbiased models. We also propose an extension of these results that leads to the fascinating possibility to extract, only from topological data, the `hidden variables' underlying network organization, making them `no more hidden'. We test our method on the World Trade Web data, where we recover the empirical Gross Domestic Product using only topological information.