State Aggregations in Markov Chains and Block Models of Networks.

@article{Faccin2021StateAI,
  title={State Aggregations in Markov Chains and Block Models of Networks.},
  author={Mauro Faccin and Michael T. Schaub and Jean-Charles Delvenne},
  journal={Physical review letters},
  year={2021},
  volume={127 7},
  pages={
          078301
        }
}
We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T=1 this recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, which enables us to explain certain features of the likelihood landscape of this generative… 

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