Null models and complexity science: disentangling signal from noise in complex interacting systems

The constantly increasing availability of fine-grained data has led to a very detailed description of many socio-economic systems (such as financial markets, interbank loans or supply chains), whose representation, however, quickly becomes too complex to allow for any meaningful intuition or insight about their functioning mechanisms. This, in turn, leads to the challenge of disentangling statistically meaningful information from noise without assuming any a priori knowledge on the particular system under study. The aim of this thesis is to develop and test on real world data unsupervised techniques to extract relevant information from large complex interacting systems. The question I try to answer is the following: is it possible to disentangle statistically relevant information from noise without assuming any prior knowledge about the system under study? In particular, I tackle this challenge from the viewpoint of hypothesis testing by developing techniques based on so-called null models, i.e., partially randomised representations of the system under study. Given that complex systems can be analysed both from the perspective of their time evolution and of their time-aggregated properties, I have tested and developed one technique for each of these two purposes. The first technique I have developed is aimed at extracting “backbones” of relevant relationships in complex interacting systems represented as static weighted networks of pairwise interactions and it is inspired by the well-known Pólya urn combinatorial process. The second technique I have developed is instead aimed at identifying statistically relevant events and temporal patterns in single or multiple time series by means of maximum entropy null models based on Ensemble Theory. Both of these methodologies try to exploit the heterogeneity of complex systems data in order to design null models that are tailored to the systems under study, and therefore capable of identifying signals that are genuinely distinctive of the systems themselves

Weight thresholding on complex networks

Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph-theoretical methods. We show that the group structure of real weighted networks is very robust under weight thresholding, as it is maintained even when most of the edges are removed. This appears to be related to the correlation between topology and weight that characterizes real networks. On the other hand, the behavior of other properties is generally system dependent