Tiago de Paula Peixoto

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  Modeling sequences and temporal networks with dynamic community structures
  Tiago de Paula Peixoto
  To reveal the mechanisms that shape the dynamics on and formation of complex systems, researchers use community-detection methods to describe large-scale patterns in their networks of interactions. Only recently have researchers proposed methods that capture essential memory effects in the dynamics and temporal changes in the formation. However, current memory methods are limited to second-order Markov chain models and current temporal methods are limited to static descriptions in time windows of continuous changes. These limitations raise fundamental questions: how much memory is required and how can time binning be evaded for efficient descriptions based on statistical evidence?
  
  We propose a dynamical description of large-scale structures in sequences and temporal networks that detects the most regularity in the data without any time binning. Our principled approach is based on the statistical inference of generative models, and generalizes the stochastic block model to edge placement probabilities that vary in time and follow an arbitrary-order hidden Markov chain. The method is fully nonparametric and can be used to detect the appropriate Markov order from data alone as well as the number of communities, without overfitting. The method can also predict future network evolution from past observations.