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| Type | Conference Presentation |
| Scope | Discipline-based scholarship |
| Title | Idiosyncratic correlations and non-Gaussian distributions in network data |
| Organization Unit | |
| Authors |
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| Presentation Type | speech |
| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Event Title | Conference on Complex Systems 2017 |
| Event Type | conference |
| Event Location | Cancun, Mexico |
| Event Start Date | September 17 - 2017 |
| Event End Date | September 22 - 2017 |
| Abstract Text | During the last decades, complex social, economical and biological systems have been studied using agent-based models (ABM). ABM are a powerful tool to discover analytic truths at the macroscopic-level when simple rules at the agent-agent interaction level are assumed. Despite great achievements in discovering analytic truths in complex systems and a large number of large datasets. Statistical models aimed to discover factual truths in complex systems have not reached the rigorous approach of econometrics models. In this paper, we introduce a network model, power law random graph model (PRGM) formulated at the agent-agent interaction level via the concept of q-conditional independence where q can be interpreted as idiosyncratic correlations or an interaction term between well-defined social mechanisms. We show that the exponential random graph models (ERGM) are the subclass of PRGM with q = 1. Motivated by the derivation of ERGM via the Boltzmann-Shannon entropy by Park and Newman, we present a second formulation of the PRGM via Tsallis entropy. Next, we construct a subclass of PRGM, called q-Markov graph models, defined by simple dependency assumptions and that violates Gaussian approximation of the network statistics. The violation of Gaussian approximation is caused by competitive social mechanisms, and it enriches PRGM with distributions ranging from bimodal, skewed and flat. Our findings open the question What warrants Gaussian approximations used to justify factual evidence in complex systems? Finally, with the help of the subclass q-Bernoulli random graph models and using two networks datasets of friendships between students in classrooms in Switzerland and the US, we show how the idiosyncratic correlation q helps to address the problem of models placing too much probability mass around a few type of networks. Although the problem of placing too much probability is well documented in poor-fitting network models, we show that this problem is inherited from the exponential decay of rare events in ERGM, and it occurs in poor-fitting- as well as overfitting models. |
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