State Aggregations in Markov Chains and Block Models of Networks
(2021) Physical Review Letters — Vol. 127, n° 7 (2021)
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- Authors
Faccin, Mauro 
Schaub, Michael. T
- 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 ¼ 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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Citations
Faccin, M., Schaub, Michael. T., & Delvenne, J.-C. (2021). State Aggregations in Markov Chains and Block Models of Networks. Physical Review Letters, 127(7). https://doi.org/10.1103/physrevlett.127.078301 (Original work published 2021)