title: Maximum likelihood: extracting unbiased information from complex networks.
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 with 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 longer hidden." We test our method on World Trade Web data, where we recover the empirical gross domestic product using only topological information.
authors.affiliation: Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 Siena, Italy.
authors.forename: Diego
authors.initials: D
authors.lastname: Garlaschelli
authors.forename: Maria I
authors.initials: MI
authors.lastname: Loffredo