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Inferring hidden states in a random kinetic Ising model: replica analysis
Zitatschlüssel BaRoOp14
Autor Ludovica Bachschmid Romano and Manfred Opper
Seiten P06013
Jahr 2014
Journal Journal of Statistical Mechanics: Theory and Experiment
Jahrgang 2014
Nummer 6
Zusammenfassung We consider the problem of predicting the spin states in a kinetic Ising model when spin trajectories are observed for only a finite fraction of sites. In a Bayesian setting, where the probabilistic model of the spin dynamics is assumed to be known, the optimal prediction can be computed from the conditional (posterior) distribution of unobserved spins given the observed ones. Using the replica method, we compute the error of the Bayes optimal predictor for parallel discrete time dynamics in a fully connected spin system with non-symmetric random couplings. The results, exact in the thermodynamic limit, agree very well with simulations of finite spin systems.
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