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State aggregations in Markov chains and block models of networks
Faccin, M.; Schaub, M.T.; Delvenne, J.-C. (2021). State aggregations in Markov chains and block models of networks. Phys. Rev. Lett. 127(7): 078301. https://dx.doi.org/10.1103/PhysRevLett.127.078301
In: Physical Review Letters. American Physical Society: Woodbury, N.Y., etc.. ISSN 0031-9007; e-ISSN 1079-7114, meer
Peer reviewed article  
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  • Faccin, M., meer
  • Schaub, M.T.
  • Delvenne, J.-C., meer
Abstract
    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 network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a timescale T ≫ 1 is essential. We demonstrate our results using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.
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